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Local triviality of equivariant algebras
Author(s) -
Skryabin Serge
Publication year - 2011
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/bdq108
Subject(s) - mathematics , triviality , residue field , pure mathematics , hopf algebra , ring (chemistry) , modulo , algebraically closed field , commutative ring , noetherian ring , maximal ideal , ideal (ethics) , field (mathematics) , algebra over a field , discrete mathematics , commutative property , philosophy , chemistry , organic chemistry , epistemology
We consider a finite algebra A over a commutative ring R . It is assumed that R is an algebra over the ground field k and that a cocommutative Hopf algebra H acts on R and A in a compatible way. This paper answers the question as to when it is possible to find a ring extension R → R ′ such that the R ′‐algebra A ⊗ R R ′ is isomorphic with A 0 ⊗ k R ′ for some k ‐algebra A 0 and the ring R ′⊗ R R is faithfully flat over the local ring R either for a single prime ideal of R containing no H ‐stable ideals of R or for all such primes. If k is algebraically closed, it is shown that A has isomorphic reductions modulo any pair of maximal ideals of R with residue field k containing the same H ‐stable ideals of R .