Get quick answers to your questions about the article from our AI researcher chatbot
{'id': 'https://openalex.org/W3037944244', 'doi': 'https://doi.org/10.5802/aif.3526', 'title': 'Explicit uniform bounds for Brauer groups of singular K3 surfaces', 'display_name': 'Explicit uniform bounds for Brauer groups of singular K3 surfaces', 'publication_year': 2023, 'publication_date': '2023-05-12', 'ids': {'openalex': 'https://openalex.org/W3037944244', 'doi': 'https://doi.org/10.5802/aif.3526', 'mag': '3037944244'}, 'language': 'en', 'primary_location': {'is_oa': True, 'landing_page_url': 'https://doi.org/10.5802/aif.3526', 'pdf_url': 'https://aif.centre-mersenne.org/item/10.5802/aif.3526.pdf', 'source': {'id': 'https://openalex.org/S78118978', 'display_name': 'Annales de l’institut Fourier', 'issn_l': '0373-0956', 'issn': ['0373-0956', '1777-5310'], 'is_oa': True, 'is_in_doaj': False, 'is_core': True, 'host_organization': 'https://openalex.org/P4323830084', 'host_organization_name': 'Association of the Annals of the Fourier Institute', 'host_organization_lineage': ['https://openalex.org/P4323830084'], 'host_organization_lineage_names': ['Association of the Annals of the Fourier Institute'], 'type': 'journal'}, 'license': None, 'license_id': None, 'version': 'publishedVersion', 'is_accepted': True, 'is_published': True}, 'type': 'article', 'type_crossref': 'journal-article', 'indexed_in': ['crossref'], 'open_access': {'is_oa': True, 'oa_status': 'gold', 'oa_url': 'https://aif.centre-mersenne.org/item/10.5802/aif.3526.pdf', 'any_repository_has_fulltext': True}, 'authorships': [{'author_position': 'first', 'author': {'id': 'https://openalex.org/A5051550520', 'display_name': 'Francesca Balestrieri', 'orcid': 'https://orcid.org/0000-0002-8710-5301'}, 'institutions': [{'id': 'https://openalex.org/I130238516', 'display_name': 'University of Minnesota', 'ror': 'https://ror.org/017zqws13', 'country_code': 'US', 'type': 'education', 'lineage': ['https://openalex.org/I130238516']}, {'id': 'https://openalex.org/I71052956', 'display_name': 'University of Reading', 'ror': 'https://ror.org/05v62cm79', 'country_code': 'GB', 'type': 'education', 'lineage': ['https://openalex.org/I71052956']}, {'id': 'https://openalex.org/I24240610', 'display_name': 'American University of Paris', 'ror': 'https://ror.org/05t197591', 'country_code': 'FR', 'type': 'education', 'lineage': ['https://openalex.org/I24240610']}], 'countries': ['FR', 'GB', 'US'], 'is_corresponding': False, 'raw_author_name': 'Francesca Balestrieri', 'raw_affiliation_strings': ['American University of Paris, 5 Boulevard de La Tour-Maubourg, 75007 Paris, France', 'Department of Mathematics, University of Minnesota, 206 Church St SE, Minneapolis, MN 55455, USA', 'University of Reading, Department of Mathematics and Statis-tics, Pepper Lane, Whiteknights, Reading RG6 6AX, UK'], 'affiliations': [{'raw_affiliation_string': 'Department of Mathematics, University of Minnesota, 206 Church St SE, Minneapolis, MN 55455, USA', 'institution_ids': ['https://openalex.org/I130238516']}, {'raw_affiliation_string': 'University of Reading, Department of Mathematics and Statis-tics, Pepper Lane, Whiteknights, Reading RG6 6AX, UK', 'institution_ids': ['https://openalex.org/I71052956']}, {'raw_affiliation_string': 'American University of Paris, 5 Boulevard de La Tour-Maubourg, 75007 Paris, France', 'institution_ids': ['https://openalex.org/I24240610']}]}, {'author_position': 'middle', 'author': {'id': 'https://openalex.org/A5041812155', 'display_name': 'Alexis Johnson', 'orcid': None}, 'institutions': [{'id': 'https://openalex.org/I130238516', 'display_name': 'University of Minnesota', 'ror': 'https://ror.org/017zqws13', 'country_code': 'US', 'type': 'education', 'lineage': ['https://openalex.org/I130238516']}, {'id': 'https://openalex.org/I71052956', 'display_name': 'University of Reading', 'ror': 'https://ror.org/05v62cm79', 'country_code': 'GB', 'type': 'education', 'lineage': ['https://openalex.org/I71052956']}, {'id': 'https://openalex.org/I24240610', 'display_name': 'American University of Paris', 'ror': 'https://ror.org/05t197591', 'country_code': 'FR', 'type': 'education', 'lineage': ['https://openalex.org/I24240610']}], 'countries': ['FR', 'GB', 'US'], 'is_corresponding': False, 'raw_author_name': 'Alexis Johnson', 'raw_affiliation_strings': ['American University of Paris, 5 Boulevard de La Tour-Maubourg, 75007 Paris, France', 'Department of Mathematics, University of Minnesota, 206 Church St SE, Minneapolis, MN 55455, USA', 'University of Reading, Department of Mathematics and Statis-tics, Pepper Lane, Whiteknights, Reading RG6 6AX, UK'], 'affiliations': [{'raw_affiliation_string': 'Department of Mathematics, University of Minnesota, 206 Church St SE, Minneapolis, MN 55455, USA', 'institution_ids': ['https://openalex.org/I130238516']}, {'raw_affiliation_string': 'University of Reading, Department of Mathematics and Statis-tics, Pepper Lane, Whiteknights, Reading RG6 6AX, UK', 'institution_ids': ['https://openalex.org/I71052956']}, {'raw_affiliation_string': 'American University of Paris, 5 Boulevard de La Tour-Maubourg, 75007 Paris, France', 'institution_ids': ['https://openalex.org/I24240610']}]}, {'author_position': 'last', 'author': {'id': 'https://openalex.org/A5056029659', 'display_name': 'Rachel Newton', 'orcid': 'https://orcid.org/0000-0003-4848-3083'}, 'institutions': [{'id': 'https://openalex.org/I130238516', 'display_name': 'University of Minnesota', 'ror': 'https://ror.org/017zqws13', 'country_code': 'US', 'type': 'education', 'lineage': ['https://openalex.org/I130238516']}, {'id': 'https://openalex.org/I71052956', 'display_name': 'University of Reading', 'ror': 'https://ror.org/05v62cm79', 'country_code': 'GB', 'type': 'education', 'lineage': ['https://openalex.org/I71052956']}, {'id': 'https://openalex.org/I24240610', 'display_name': 'American University of Paris', 'ror': 'https://ror.org/05t197591', 'country_code': 'FR', 'type': 'education', 'lineage': ['https://openalex.org/I24240610']}], 'countries': ['FR', 'GB', 'US'], 'is_corresponding': False, 'raw_author_name': 'Rachel Newton', 'raw_affiliation_strings': ['American University of Paris, 5 Boulevard de La Tour-Maubourg, 75007 Paris, France', 'Department of Mathematics, University of Minnesota, 206 Church St SE, Minneapolis, MN 55455, USA', 'University of Reading, Department of Mathematics and Statis-tics, Pepper Lane, Whiteknights, Reading RG6 6AX, UK'], 'affiliations': [{'raw_affiliation_string': 'Department of Mathematics, University of Minnesota, 206 Church St SE, Minneapolis, MN 55455, USA', 'institution_ids': ['https://openalex.org/I130238516']}, {'raw_affiliation_string': 'University of Reading, Department of Mathematics and Statis-tics, Pepper Lane, Whiteknights, Reading RG6 6AX, UK', 'institution_ids': ['https://openalex.org/I71052956']}, {'raw_affiliation_string': 'American University of Paris, 5 Boulevard de La Tour-Maubourg, 75007 Paris, France', 'institution_ids': ['https://openalex.org/I24240610']}]}], 'countries_distinct_count': 3, 'institutions_distinct_count': 3, 'corresponding_author_ids': [], 'corresponding_institution_ids': [], 'apc_list': None, 'apc_paid': None, 'fwci': 0.0, 'has_fulltext': True, 'fulltext_origin': 'pdf', 'cited_by_count': 0, 'citation_normalized_percentile': {'value': 0.0, 'is_in_top_1_percent': False, 'is_in_top_10_percent': False}, 'cited_by_percentile_year': {'min': 0, 'max': 71}, 'biblio': {'volume': '73', 'issue': '2', 'first_page': '567', 'last_page': '607'}, 'is_retracted': False, 'is_paratext': False, 'primary_topic': {'id': 'https://openalex.org/T10061', 'display_name': 'Algebraic Geometry and Moduli Theory', 'score': 0.9998, 'subfield': {'id': 'https://openalex.org/subfields/2608', 'display_name': 'Geometry and Topology'}, 'field': {'id': 'https://openalex.org/fields/26', 'display_name': 'Mathematics'}, 'domain': {'id': 'https://openalex.org/domains/3', 'display_name': 'Physical Sciences'}}, 'topics': [{'id': 'https://openalex.org/T10061', 'display_name': 'Algebraic Geometry and Moduli Theory', 'score': 0.9998, 'subfield': {'id': 'https://openalex.org/subfields/2608', 'display_name': 'Geometry and Topology'}, 'field': {'id': 'https://openalex.org/fields/26', 'display_name': 'Mathematics'}, 'domain': {'id': 'https://openalex.org/domains/3', 'display_name': 'Physical Sciences'}}, {'id': 'https://openalex.org/T11130', 'display_name': 'Cryptography and Error-Correcting Codes', 'score': 0.9913, 'subfield': {'id': 'https://openalex.org/subfields/1702', 'display_name': 'Artificial Intelligence'}, 'field': {'id': 'https://openalex.org/fields/17', 'display_name': 'Computer Science'}, 'domain': {'id': 'https://openalex.org/domains/3', 'display_name': 'Physical Sciences'}}, {'id': 'https://openalex.org/T11680', 'display_name': 'Proofs of Langlands Conjectures for GL(n)', 'score': 0.9755, 'subfield': {'id': 'https://openalex.org/subfields/2610', 'display_name': 'Mathematical Physics'}, 'field': {'id': 'https://openalex.org/fields/26', 'display_name': 'Mathematics'}, 'domain': {'id': 'https://openalex.org/domains/3', 'display_name': 'Physical Sciences'}}], 'keywords': [{'id': 'https://openalex.org/keywords/isomorphism', 'display_name': 'Isomorphism (crystallography)', 'score': 0.6524196}, {'id': 'https://openalex.org/keywords/birational-geometry', 'display_name': 'Birational Geometry', 'score': 0.473731}, {'id': 'https://openalex.org/keywords/lattice', 'display_name': 'Lattice (music)', 'score': 0.42665586}], 'concepts': [{'id': 'https://openalex.org/C33923547', 'wikidata': 'https://www.wikidata.org/wiki/Q395', 'display_name': 'Mathematics', 'level': 0, 'score': 0.8831756}, {'id': 'https://openalex.org/C62196294', 'wikidata': 'https://www.wikidata.org/wiki/Q900456', 'display_name': 'Brauer group', 'level': 2, 'score': 0.7109467}, {'id': 'https://openalex.org/C203436722', 'wikidata': 'https://www.wikidata.org/wiki/Q902950', 'display_name': 'Isomorphism (crystallography)', 'level': 3, 'score': 0.6524196}, {'id': 'https://openalex.org/C12657307', 'wikidata': 'https://www.wikidata.org/wiki/Q616608', 'display_name': 'Algebraic number field', 'level': 2, 'score': 0.6146922}, {'id': 'https://openalex.org/C78397625', 'wikidata': 'https://www.wikidata.org/wiki/Q192487', 'display_name': 'Discriminant', 'level': 2, 'score': 0.5703096}, {'id': 'https://openalex.org/C202444582', 'wikidata': 'https://www.wikidata.org/wiki/Q837863', 'display_name': 'Pure mathematics', 'level': 1, 'score': 0.55764395}, {'id': 'https://openalex.org/C2780990831', 'wikidata': 'https://www.wikidata.org/wiki/Q319141', 'display_name': 'Conjecture', 'level': 2, 'score': 0.55165136}, {'id': 'https://openalex.org/C179603306', 'wikidata': 'https://www.wikidata.org/wiki/Q268493', 'display_name': 'Elliptic curve', 'level': 2, 'score': 0.44464508}, {'id': 'https://openalex.org/C77553402', 'wikidata': 'https://www.wikidata.org/wiki/Q13222579', 'display_name': 'Upper and lower bounds', 'level': 2, 'score': 0.4443215}, {'id': 'https://openalex.org/C2781204021', 'wikidata': 'https://www.wikidata.org/wiki/Q6497091', 'display_name': 'Lattice (music)', 'level': 2, 'score': 0.42665586}, {'id': 'https://openalex.org/C90673727', 'wikidata': 'https://www.wikidata.org/wiki/Q901718', 'display_name': 'Product (mathematics)', 'level': 2, 'score': 0.4128147}, {'id': 'https://openalex.org/C114614502', 'wikidata': 'https://www.wikidata.org/wiki/Q76592', 'display_name': 'Combinatorics', 'level': 1, 'score': 0.3749116}, {'id': 'https://openalex.org/C134306372', 'wikidata': 'https://www.wikidata.org/wiki/Q7754', 'display_name': 'Mathematical analysis', 'level': 1, 'score': 0.18771964}, {'id': 'https://openalex.org/C2524010', 'wikidata': 'https://www.wikidata.org/wiki/Q8087', 'display_name': 'Geometry', 'level': 1, 'score': 0.11178717}, {'id': 'https://openalex.org/C185592680', 'wikidata': 'https://www.wikidata.org/wiki/Q2329', 'display_name': 'Chemistry', 'level': 0, 'score': 0.0}, {'id': 'https://openalex.org/C121332964', 'wikidata': 'https://www.wikidata.org/wiki/Q413', 'display_name': 'Physics', 'level': 0, 'score': 0.0}, {'id': 'https://openalex.org/C154945302', 'wikidata': 'https://www.wikidata.org/wiki/Q11660', 'display_name': 'Artificial intelligence', 'level': 1, 'score': 0.0}, {'id': 'https://openalex.org/C41008148', 'wikidata': 'https://www.wikidata.org/wiki/Q21198', 'display_name': 'Computer science', 'level': 0, 'score': 0.0}, {'id': 'https://openalex.org/C24890656', 'wikidata': 'https://www.wikidata.org/wiki/Q82811', 'display_name': 'Acoustics', 'level': 1, 'score': 0.0}, {'id': 'https://openalex.org/C115624301', 'wikidata': 'https://www.wikidata.org/wiki/Q895901', 'display_name': 'Crystal structure', 'level': 2, 'score': 0.0}, {'id': 'https://openalex.org/C8010536', 'wikidata': 'https://www.wikidata.org/wiki/Q160398', 'display_name': 'Crystallography', 'level': 1, 'score': 0.0}], 'mesh': [], 'locations_count': 3, 'locations': [{'is_oa': True, 'landing_page_url': 'https://doi.org/10.5802/aif.3526', 'pdf_url': 'https://aif.centre-mersenne.org/item/10.5802/aif.3526.pdf', 'source': {'id': 'https://openalex.org/S78118978', 'display_name': 'Annales de l’institut Fourier', 'issn_l': '0373-0956', 'issn': ['0373-0956', '1777-5310'], 'is_oa': True, 'is_in_doaj': False, 'is_core': True, 'host_organization': 'https://openalex.org/P4323830084', 'host_organization_name': 'Association of the Annals of the Fourier Institute', 'host_organization_lineage': ['https://openalex.org/P4323830084'], 'host_organization_lineage_names': ['Association of the Annals of the Fourier Institute'], 'type': 'journal'}, 'license': None, 'license_id': None, 'version': 'publishedVersion', 'is_accepted': True, 'is_published': True}, {'is_oa': True, 'landing_page_url': 'https://centaur.reading.ac.uk/99898/1/UniformBounds_AIF_FinalVersion_arxiv.pdf', 'pdf_url': 'https://centaur.reading.ac.uk/99898/1/UniformBounds_AIF_FinalVersion_arxiv.pdf', 'source': {'id': 'https://openalex.org/S4306402273', 'display_name': 'CentAUR (University of Reading)', 'issn_l': None, 'issn': None, 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/I71052956', 'host_organization_name': 'University of Reading', 'host_organization_lineage': ['https://openalex.org/I71052956'], 'host_organization_lineage_names': ['University of Reading'], 'type': 'repository'}, 'license': None, 'license_id': None, 'version': 'acceptedVersion', 'is_accepted': True, 'is_published': False}, {'is_oa': True, 'landing_page_url': 'https://arxiv.org/abs/2006.14907', 'pdf_url': 'https://arxiv.org/pdf/2006.14907', 'source': {'id': 'https://openalex.org/S4306400194', 'display_name': 'arXiv (Cornell University)', 'issn_l': None, 'issn': None, 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/I205783295', 'host_organization_name': 'Cornell University', 'host_organization_lineage': ['https://openalex.org/I205783295'], 'host_organization_lineage_names': ['Cornell University'], 'type': 'repository'}, 'license': None, 'license_id': None, 'version': 'submittedVersion', 'is_accepted': False, 'is_published': False}], 'best_oa_location': {'is_oa': True, 'landing_page_url': 'https://doi.org/10.5802/aif.3526', 'pdf_url': 'https://aif.centre-mersenne.org/item/10.5802/aif.3526.pdf', 'source': {'id': 'https://openalex.org/S78118978', 'display_name': 'Annales de l’institut Fourier', 'issn_l': '0373-0956', 'issn': ['0373-0956', '1777-5310'], 'is_oa': True, 'is_in_doaj': False, 'is_core': True, 'host_organization': 'https://openalex.org/P4323830084', 'host_organization_name': 'Association of the Annals of the Fourier Institute', 'host_organization_lineage': ['https://openalex.org/P4323830084'], 'host_organization_lineage_names': ['Association of the Annals of the Fourier Institute'], 'type': 'journal'}, 'license': None, 'license_id': None, 'version': 'publishedVersion', 'is_accepted': True, 'is_published': True}, 'sustainable_development_goals': [{'score': 0.68, 'display_name': 'Reduced inequalities', 'id': 'https://metadata.un.org/sdg/10'}], 'grants': [], 'datasets': [], 'versions': [], 'referenced_works_count': 41, 'referenced_works': ['https://openalex.org/W137936283', 'https://openalex.org/W1586485728', 'https://openalex.org/W1619171454', 'https://openalex.org/W1911865901', 'https://openalex.org/W1969583401', 'https://openalex.org/W1976982814', 'https://openalex.org/W2050019333', 'https://openalex.org/W205288789', 'https://openalex.org/W2061710893', 'https://openalex.org/W2092045774', 'https://openalex.org/W2116301670', 'https://openalex.org/W2135491218', 'https://openalex.org/W2139787113', 'https://openalex.org/W2159863838', 'https://openalex.org/W2174389065', 'https://openalex.org/W2208916667', 'https://openalex.org/W2466446368', 'https://openalex.org/W2490704775', 'https://openalex.org/W2531879069', 'https://openalex.org/W2586914953', 'https://openalex.org/W2735504512', 'https://openalex.org/W2798959868', 'https://openalex.org/W2884621701', 'https://openalex.org/W2962693456', 'https://openalex.org/W2963751279', 'https://openalex.org/W2963776088', 'https://openalex.org/W2963860528', 'https://openalex.org/W2964045414', 'https://openalex.org/W2964257661', 'https://openalex.org/W3007836994', 'https://openalex.org/W3036660682', 'https://openalex.org/W3095195414', 'https://openalex.org/W3101428986', 'https://openalex.org/W3102436584', 'https://openalex.org/W3106479979', 'https://openalex.org/W3163398941', 'https://openalex.org/W3204944553', 'https://openalex.org/W4249780871', 'https://openalex.org/W4294564067', 'https://openalex.org/W66820687', 'https://openalex.org/W950944387'], 'related_works': ['https://openalex.org/W4300237203', 'https://openalex.org/W3188882553', 'https://openalex.org/W3098250786', 'https://openalex.org/W3037944244', 'https://openalex.org/W3026358768', 'https://openalex.org/W2897153210', 'https://openalex.org/W2319134944', 'https://openalex.org/W2005973892', 'https://openalex.org/W1998742353', 'https://openalex.org/W1654758774'], 'abstract_inverted_index': {'Let': [0], 'k': [1], 'be': [2, 89], 'a': [3, 30, 44, 62, 98], 'number': [4, 106], 'field.': [5], 'We': [6], 'give': [7], 'an': [8, 52, 119], 'explicit': [9, 75], 'bound,': [10, 99], 'depending': [11, 100], 'only': [12, 78, 101], 'on': [13, 22, 68, 79, 102, 104], '[k:ℚ]': [14, 80], 'and': [15, 81], 'the': [16, 19, 23, 26, 39, 57, 74, 83, 86, 105, 123], 'discriminant': [17], 'of': [18, 25, 29, 46, 107, 110, 122], 'Néron–Severi': [20], 'lattice,': [21], 'size': [24], 'Brauer': [27], 'group': [28], 'K3': [31, 112, 129], 'surface': [32, 41], 'X/k': [33], 'that': [34, 56, 85], 'is': [35, 64], 'geometrically': [36], 'isomorphic': [37], 'to': [38, 43, 96], 'Kummer': [40], 'attached': [42], 'product': [45], 'isogenous': [47], 'CM': [48], 'elliptic': [49, 87], 'curves.': [50], 'As': [51], 'application,': [53], 'we': [54, 70, 93], 'show': [55, 94], 'Brauer–Manin': [58], 'set': [59], 'for': [60, 127], 'such': [61], 'variety': [63], 'effectively': [65], 'computable.': [66], 'Conditional': [67], 'GRH,': [69], 'can': [71], 'also': [72], 'make': [73], 'bound': [76], 'depend': [77], 'remove': [82], 'condition': [84], 'curves': [88], 'isogenous.': [90], 'In': [91], 'addition,': [92], 'how': [95], 'obtain': [97], '[k:ℚ],': [103], 'C-isomorphism': [108], 'classes': [109], 'singular': [111, 128], 'surfaces': [113], 'defined': [114], 'over': [115], 'k,': [116], 'thus': [117], 'proving': [118], 'effective': [120], 'version': [121], 'strong': [124], 'Shafarevich': [125], 'conjecture': [126], 'surfaces.': [130]}, 'cited_by_api_url': 'https://api.openalex.org/works?filter=cites:W3037944244', 'counts_by_year': [], 'updated_date': '2024-09-09T16:40:38.705443', 'created_date': '2020-07-02'}