Title: The Spectrum of an Equivariant Cohomology Ring: I
Abstract:Let G be a compact Lie group (e.g., a finite group) and let HG= H*(BG, Z/pZ) be its mod p cohomology ring. One knows this ring is finitely generated, hence upon dividing out by the ideal of nilpotent ...Let G be a compact Lie group (e.g., a finite group) and let HG= H*(BG, Z/pZ) be its mod p cohomology ring. One knows this ring is finitely generated, hence upon dividing out by the ideal of nilpotent elements it becomes a finitely generated commutative algebra over the field Z/pZ. It is the purpose of this series of papers to relate the invariants attached to such a ring by commutative algebra to the family of elementary abelian p-subgroups of G. For example we prove a conjecture of Atiyah and Swan to the effect that the Krull dimension of the ring equals the maximum rank of an elementary abelian p-subgroup. Another result, which will appear in part II, asserts that the minimal prime ideals of the ring are in one-one correspondence with the conjugacy classes of maximal elementary abelian p-subgroups. Actually the theorems of the series are formulated more generally for the equivariant cohomology ring of a G-space X, defined by the formulaRead More
Publication Year: 1971
Publication Date: 1971-11-01
Language: en
Type: article
Indexed In: ['crossref']
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Cited By Count: 647
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