Bloch-Kato conjecture and motivic cohomology with finite coefficients
ثبت نشده
چکیده
منابع مشابه
An Overview of Motivic Cohomology
In this talk we give an overview of some of the motivations behind and applications of motivic cohomology.We first present aK-theoretic timeline converging onmotivic cohomology, then briefly discuss algebraic K-theory and its more concrete cousin Milnor K-theory. We then present a geometric definition of motivic cohomology via Bloch’s higher Chow groups and outline the main features of motivic ...
متن کامل. A G ] 2 2 Ja n 20 09 A p - ADIC REGULATOR MAP AND FINITENESS RESULTS FOR ARITHMETIC SCHEMES 1
A main theme of the paper is a conjecture of Bloch-Kato on the image of padic regulator maps for a proper smooth variety X over an algebraic number field k. The conjecture for a regulator map of particular degree and weight is related to finiteness of two arithmetic objects: One is the p-primary torsion part of the Chow group in codimension 2 of X . Another is an unramified cohomology group of ...
متن کاملNorm Varieties
For given symbol in the n-th Milnor K-group modulo prime l we construct a splitting variety with several properties. This variety is lgeneric, meaning that it is generic with respect to splitting fields having no finite extensions of degree prime to l. The degree of its top Milnor class is not divisible by l2, and a certain motivic cohomology group of this variety consists of units. The existen...
متن کاملTowards Connectivity for Codimension 2 Cycles: Infinitesimal Deformations
Let X be a smooth projective variety over an algebraically closed field k ⊂ C of characteristic zero, and Y ⊂ X a smooth complete intersection. The Weak Lefschetz theorem states that the natural restriction map H(X(C), Q) → H(Y (C), Q) on singular cohomology is an isomorphism for all i < dim(Y ). The Bloch-Beilinson conjectures on the existence of certain filtrations on Chow groups combined wit...
متن کاملOn the Local Tamagawa Number Conjecture for Tate Motives over Tamely Ramified Fields
The local Tamagawa number conjecture, which was first formulated by Fontaine and Perrin-Riou, expresses the compatibility of the (global) Tamagawa number conjecture on motivic L-functions with the functional equation. The local conjecture was proven for Tate motives over finite unramified extensions K/Qp by Bloch and Kato. We use the theory of (φ,Γ)-modules and a reciprocity law due to Cherbonn...
متن کامل