Cohomological Hasse principle and motivic cohomology for arithmetic schemes

DOI10.1007/s10240-011-0038-yzbMath1263.14026arXiv1010.5930OpenAlexW2151773998MaRDI QIDQ691688

Moritz Kerz, Shuji Saito

Publication date: 3 December 2012

Published in: Publications Mathématiques (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1010.5930

zbMATH Keywords

motivic cohomologyarithmetic schemecohomological Hasse principle

Mathematics Subject Classification ID

(K)-theory and homology; cyclic homology and cohomology (19D55) Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) (14G10) Local ground fields in algebraic geometry (14G20) Arithmetic varieties and schemes; Arakelov theory; heights (14G40) Motivic cohomology; motivic homotopy theory (14F42) Abelian varieties and schemes (14K99)

Related Items (16)

Tame class field theory for singular varieties over finite fields ⋮ The kernel of the reciprocity map of simple normal crossing varieties over finite fields ⋮ Refined unramified cohomology of schemes ⋮ Motivic homology and class field theory over \(p\)-adic fields ⋮ On integral class field theory for varieties over \(p\)-adic fields ⋮ HIGHER IDELES AND CLASS FIELD THEORY ⋮ Finiteness theorems for the shifted Witt and higher Grothendieck-Witt groups of arithmetic schemes ⋮ A local to global principle for higher zero-cycles ⋮ Cohomological Hasse principle and motivic cohomology for arithmetic schemes ⋮ On the Chow groups of certain geometrically rational 5-folds ⋮ Motivic cohomology: applications and conjectures ⋮ Hasse principles for higher-dimensional fields ⋮ Sums of squares in function fields over Henselian local fields ⋮ TATE’S CONJECTURE AND THE TATE–SHAFAREVICH GROUP OVER GLOBAL FUNCTION FIELDS ⋮ Local–global principles for curves over semi‐global fields ⋮ Topology of nonarchimedean analytic spaces and relations to complex algebraic geometry

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