Search results for "Valuation ring"

showing 2 items of 2 documents

Towards Vorst's conjecture in positive characteristic

2018

Vorst's conjecture relates the regularity of a ring with the $\mathbb{A}^1$-homotopy invariance of its $K$-theory. We show a variant of this conjecture in positive characteristic.

CombinatoricsMathematics - Algebraic GeometryRing (mathematics)Algebra and Number TheoryConjectureMathematics::K-Theory and HomologyMathematics - K-Theory and HomologyFOS: MathematicsK-Theory and Homology (math.KT)Algebraic Geometry (math.AG)Valuation ringMathematicsCompositio Mathematica
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On the blockwise modular isomorphism problem

2017

As a generalization of the modular isomorphism problem we study the behavior of defect groups under Morita equivalence of blocks of finite groups over algebraically closed fields of positive characteristic. We prove that the Morita equivalence class of a block B of defect at most 3 determines the defect groups of B up to isomorphism. In characteristic 0 we prove similar results for metacyclic defect groups and 2-blocks of defect 4. In the second part of the paper we investigate the situation for p-solvable groups G. Among other results we show that the group algebra of G itself determines if G has abelian Sylow p-subgroups.

Pure mathematicsGeneral Mathematics010102 general mathematicsSylow theoremsBlock (permutation group theory)Group algebra01 natural sciencesValuation ring0103 physical sciencesFOS: Mathematics010307 mathematical physicsIsomorphism0101 mathematicsAbelian groupMorita equivalenceAlgebraically closed fieldRepresentation Theory (math.RT)Mathematics - Representation TheoryMathematics
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