On the Weil-\'etale cohomology of number fields

Name: Work Video:
Duration: 3 min 30 s
Description: We give a direct description of the category of sheaves on Lichtenbaum's Weil-etale site of a number ring. Then we apply this result to define a spectral sequence relating Weil-etale cohomology to Artin-Verdier etale cohomology. Finally we construct complexes of etale sheaves computing the expected Weil-etale cohomology.
Baptiste Morin
{'id': 'https://openalex.org/W2953389228', 'doi': None, 'title': "On the Weil-\\'etale cohomology of number fields", 'display_name': "On the Weil-\\'etale cohomology of number fields", 'publication_year': 2010, 'publication_date': '2010-06-02', 'ids': {'openalex': 'https://openalex.org/W2953389228', 'mag': '2953389228'}, 'language': 'en', 'primary_location': {'is_oa': False, 'landing_page_url': 'https://arxiv.org/pdf/1006.0521', 'pdf_url': None, '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}, 'type': 'preprint', 'type_crossref': 'posted-content', 'indexed_in': [], 'open_access': {'is_oa': False, 'oa_status': 'closed', 'oa_url': None, 'any_repository_has_fulltext': False}, 'authorships': [{'author_position': 'first', 'author': {'id': 'https://openalex.org/A5085302584', 'display_name': 'Baptiste Morin', 'orcid': None}, 'institutions': [{'id': 'https://openalex.org/I122411786', 'display_name': 'California Institute of Technology', 'ror': 'https://ror.org/05dxps055', 'country_code': 'US', 'type': 'education', 'lineage': ['https://openalex.org/I122411786']}], 'countries': ['US'], 'is_corresponding': True, 'raw_author_name': 'Baptiste Morin', 'raw_affiliation_strings': ['Department of Mathematics, California Institute of Technology, 1200 E. California Boulevard, Pasadena, California 91125'], 'affiliations': [{'raw_affiliation_string': 'Department of Mathematics, California Institute of Technology, 1200 E. California Boulevard, Pasadena, California 91125', 'institution_ids': ['https://openalex.org/I122411786']}]}], 'institution_assertions': [], 'countries_distinct_count': 1, 'institutions_distinct_count': 1, 'corresponding_author_ids': ['https://openalex.org/A5085302584'], 'corresponding_institution_ids': ['https://openalex.org/I122411786'], 'apc_list': None, 'apc_paid': None, 'fwci': None, 'has_fulltext': False, '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': 64}, 'biblio': {'volume': None, 'issue': None, 'first_page': None, 'last_page': None}, 'is_retracted': False, 'is_paratext': False, 'primary_topic': {'id': 'https://openalex.org/T11680', 'display_name': 'Advanced Algebra and Geometry', 'score': 0.9999, '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'}}, 'topics': [{'id': 'https://openalex.org/T11680', 'display_name': 'Advanced Algebra and Geometry', 'score': 0.9999, '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'}}, {'id': 'https://openalex.org/T10061', 'display_name': 'Algebraic Geometry and Number 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/T10287', 'display_name': 'Algebraic structures and combinatorial models', 'score': 0.9997, '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'}}], 'keywords': [{'id': 'https://openalex.org/keywords/spectral-sequence', 'display_name': 'Spectral sequence', 'score': 0.5605388}], 'concepts': [{'id': 'https://openalex.org/C33923547', 'wikidata': 'https://www.wikidata.org/wiki/Q395', 'display_name': 'Mathematics', 'level': 0, 'score': 0.8082696}, {'id': 'https://openalex.org/C45442697', 'wikidata': 'https://www.wikidata.org/wiki/Q8078429', 'display_name': 'Étale cohomology', 'level': 4, 'score': 0.7740511}, {'id': 'https://openalex.org/C202444582', 'wikidata': 'https://www.wikidata.org/wiki/Q837863', 'display_name': 'Pure mathematics', 'level': 1, 'score': 0.59461886}, {'id': 'https://openalex.org/C178609977', 'wikidata': 'https://www.wikidata.org/wiki/Q3503315', 'display_name': 'Spectral sequence', 'level': 3, 'score': 0.5605388}, {'id': 'https://openalex.org/C78606066', 'wikidata': 'https://www.wikidata.org/wiki/Q1198376', 'display_name': 'Cohomology', 'level': 2, 'score': 0.5524996}, {'id': 'https://openalex.org/C155751095', 'wikidata': 'https://www.wikidata.org/wiki/Q1408937', 'display_name': 'Group cohomology', 'level': 3, 'score': 0.3234857}], 'mesh': [], 'locations_count': 1, 'locations': [{'is_oa': False, 'landing_page_url': 'https://arxiv.org/pdf/1006.0521', 'pdf_url': None, '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': None, 'sustainable_development_goals': [], 'grants': [], 'datasets': [], 'versions': [], 'referenced_works_count': 5, 'referenced_works': ['https://openalex.org/W1580630207', 'https://openalex.org/W2008195045', 'https://openalex.org/W2950629577', 'https://openalex.org/W3144374870', 'https://openalex.org/W33476533'], 'related_works': ['https://openalex.org/W3186877768', 'https://openalex.org/W3151341448', 'https://openalex.org/W2911967682', 'https://openalex.org/W2884689175', 'https://openalex.org/W2808179910', 'https://openalex.org/W2778332639', 'https://openalex.org/W2584629686', 'https://openalex.org/W2565487908', 'https://openalex.org/W2314535177', 'https://openalex.org/W2114159257', 'https://openalex.org/W2052296815', 'https://openalex.org/W2042393429', 'https://openalex.org/W2039060025', 'https://openalex.org/W2034813086', 'https://openalex.org/W1994656178', 'https://openalex.org/W1812014928', 'https://openalex.org/W1678873405', 'https://openalex.org/W1622013983', 'https://openalex.org/W1534756430', 'https://openalex.org/W130001917'], 'abstract_inverted_index': {'We': [0], 'give': [1], 'a': [2, 15, 25], 'direct': [3], 'description': [4], 'of': [5, 8, 14, 39], 'the': [6, 43], 'category': [7], 'sheaves': [9, 41], 'on': [10], "Lichtenbaum's": [11], 'Weil-etale': [12, 29, 45], 'site': [13], 'number': [16], 'ring.': [17], 'Then': [18], 'we': [19, 36], 'apply': [20], 'this': [21], 'result': [22], 'to': [23, 31], 'define': [24], 'spectral': [26], 'sequence': [27], 'relating': [28], 'cohomology': [30], 'Artin-Verdier': [32], 'etale': [33, 40], 'cohomology.': [34, 46], 'Finally': [35], 'construct': [37], 'complexes': [38], 'computing': [42], 'expected': [44]}, 'cited_by_api_url': 'https://api.openalex.org/works?filter=cites:W2953389228', 'counts_by_year': [], 'updated_date': '2024-12-12T10:15:36.373531', 'created_date': '2019-06-27'}
Publication Information

Basic Information

Access and Citation

AI Researcher Chatbot

Primary Location

Authors

Topics

Keywords

Related Works
