Motivic cohomology over Dedekind rings | Zendy

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Motivic cohomology over Dedekind rings

Author(s) -

Thomas Geisser

Publication year - 2004

Publication title -

mathematische zeitschrift

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.38

H-Index - 66

eISSN - 1432-1823

pISSN - 0025-5874

DOI - 10.1007/s00209-004-0680-x

Subject(s) - mathematics , dedekind cut , motivic cohomology , pure mathematics , cohomology , discrete valuation ring , conjecture , isomorphism (crystallography) , resolution (logic) , invertible matrix , discrete valuation , galois cohomology , holomorphic function , equivariant cohomology , de rham cohomology , galois group , crystal structure , chemistry , artificial intelligence , field (mathematics) , computer science , crystallography

We study properties of Bloch’s higher Chow groups on smooth varieties over Dedekind rings. We prove the vanishing of for i > n, and the existence of a Gersten resolution for if the residue characteristic is p. We also show that the Bloch-Kato conjecture implies the Beilinson-Lichtenbaum conjecture an identification for m invertible, and a Gersten resolution with (arbitrary) finite coefficients. Over a complete discrete valuation ring of mixed characteristic (0, p), we construct a map from motivic cohomology to syntomic cohomology, which is a quasi-isomorphism provided the Bloch-Kato conjecture holds.

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