Arithmetic homology and an integral version of Kato's conjecture

DOI10.1515/CRELLE.2010.050zbMath1211.14014arXiv0704.1192WikidataQ123146852 ScholiaQ123146852MaRDI QIDQ3579823

Thomas Geisser

Publication date: 11 August 2010

Published in: Journal für die reine und angewandte Mathematik (Crelles Journal) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0704.1192

zbMATH Keywords

Chow groupsclass field theoryarithmetic homology

Mathematics Subject Classification ID

(K)-theory and homology; cyclic homology and cohomology (19D55) Geometric class field theory (11G45) Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies) (14F43) (Equivariant) Chow groups and rings; motives (14C15) Generalized class field theory ((K)-theoretic aspects) (19F05)

Related Items

Tame class field theory for singular varieties over finite fields ⋮ On integral class field theory for varieties over \(p\)-adic fields ⋮ PONTRYAGIN DUALITY FOR VARIETIES OVER p-ADIC FIELDS ⋮ On uniqueness ofp-adic period morphisms, II ⋮ Semistable conjecture via \(K\)-theory ⋮ Cohomological Hasse principle and motivic cohomology for arithmetic schemes ⋮ Weights in arithmetic geometry ⋮ Motivic cohomology: applications and conjectures ⋮ The Brauer–Manin pairing, class field theory, and motivic homology

Cites Work

• Weil-étale cohomology over finite fields
• Algebraic cycles and higher K-theory
• Tate's conjecture, algebraic cycles and rational \(K\)-theory in characteristic \(p\)
• On the kernel of the reciprocity map of normal surfaces over finite fields
• A note on Gersten's conjecture for logarithmic Hodge-Witt sheaves
• The \(K\)-theory of fields in characteristic \(p\)
• Unramified class field theory of arithmetical surfaces
• Arithmetic cohomology over finite fields and special values of \(\zeta\)-functions
• The Weil-étale topology on schemes over finite fields