Algebraic $K$-theory and etale cohomology

Thomason, R. W.

doi:10.24033/asens.1495

Cited by 243 publications

(231 citation statements)

References 54 publications

Supporting

Mentioning

224

Contrasting

Unclassified

Order By: Relevance

“…The first statement is [16,Theorem 1.5]. For the second statement, we employ Thomason's criterion [26,Prop. 2.3].…”

Section: And Hencementioning

confidence: 99%

Motivic cohomology over Dedekind rings

Geisser

2004

Math. Z.

115

View full text Add to dashboard Cite

Abstract. We study properties of Bloch's higher Chow groups on smooth varieties over Dedekind rings. We prove a conditional Gersten resolution, which implies that H i (Z(n)) = 0 for i > n and that there is a Gersten resolution for H i (Z/p r (n)), if the residue characteristic is p. We also show that the Bloch-Kato conjecture implies the Beilinson-Lichtenbaum conjecture, an identification Z/m(n)é t ∼ = µ ⊗n m , for m invertible on the scheme, and a Gersten resolution with (arbitrary) finite coefficients. Over a 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.

show abstract

“…The first statement is [16,Theorem 1.5]. For the second statement, we employ Thomason's criterion [26,Prop. 2.3].…”

Section: And Hencementioning

confidence: 99%

Motivic cohomology over Dedekind rings

Geisser

2004

Math. Z.

115

View full text Add to dashboard Cite

show abstract

“…This paper is concerned with the subject of homotopical sheaf theory, as it has developed over time in the articles [I,B,BG,Th,Jo,J1,J2,J3,J4]. Given a fixed Grothendieck site C, one wants to consider contravariant functors F defined on C whose values have a homotopy type associated to them.…”

Section: Introductionmentioning

confidence: 99%

Hypercovers and simplicial presheaves

Dugger

Hollander

Isaksen

2004

Math. Proc. Camb. Phil. Soc.

158

212

View full text Add to dashboard Cite

Abstract. We use hypercovers to study the homotopy theory of simplicial presheaves. The main result says that model structures for simplicial presheaves involving local weak equivalences can be constructed by localizing at the hypercovers. One consequence is that the fibrant objects can be explicitly described in terms of a hypercover descent condition, and the fibrations can be described by a relative descent condition. We give a few applications for this new description of the homotopy theory of simplicial presheaves.

show abstract

“…Over C, comparison with the Atiyah-Hirzebruch spectral sequence for topological K-theory also yields examples where the Thomason descent spectral sequence of [48] does not degenerate, which strongly suggests that (1.3) should not degenerate in general (compare [50, §8] This is thanks to both Hoobler's Henselian pair trick [24] and the ThomasonTrobaugh descent theorem for the Bass extension of algebraic K-theory [51]. Theorem 3 suggests that a form of (1.3) exists even for singular schemes (I write a form because of negative K-groups, which remain mysterious at this stage), and also that Voevodsky's cdh cohomology (e.g.…”

Section: Statement Of Resultsmentioning

confidence: 99%

K-Theory of Semi-local Rings with Finite Coefficients and Étale Cohomology

Kahn¹

2002

K-Theory

View full text Add to dashboard Cite

Algebraic $K$-theory and etale cohomology

Cited by 243 publications

References 54 publications

Motivic cohomology over Dedekind rings

Motivic cohomology over Dedekind rings

Hypercovers and simplicial presheaves

K-Theory of Semi-local Rings with Finite Coefficients and Étale Cohomology

Contact Info

Product

Resources

About