Arithmetic cohomology over finite fields and special values of \(\zeta\)-functions

DOI10.1215/S0012-7094-06-13312-4zbMath1104.14011arXivmath/0405164OpenAlexW2009476677MaRDI QIDQ2496922

Thomas Geisser

Publication date: 25 July 2006

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0405164

zbMATH Keywords

Weil-étale cohomology

Mathematics Subject Classification ID

Étale and other Grothendieck topologies and (co)homologies (14F20) Varieties over finite and local fields (11G25) Motivic cohomology; motivic homotopy theory (14F42)

Related Items

SPECIAL VALUES OF THE ZETA FUNCTION OF AN ARITHMETIC SURFACE ⋮ Differential forms in positive characteristic. II: cdh-descent via functorial Riemann-Zariski spaces ⋮ THE p-COHOMOLOGY OF ALGEBRAIC VARIETIES AND SPECIAL VALUES OF ZETA FUNCTIONS ⋮ 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 ⋮ SPECIAL VALUES OF ZETA-FUNCTIONS OF REGULAR SCHEMES ⋮ Hodge-Tate decomposition for non-smooth spaces ⋮ On Geometric Iwasawa Theory and Special Values of Zeta Functions ⋮ Differential forms in positive characteristic avoiding resolution of singularities ⋮ Compatibility of special value conjectures with the functional equation of zeta functions ⋮ Milne's correcting factor and derived de Rham cohomology. II ⋮ Cohomological Hasse principle and motivic cohomology for arithmetic schemes ⋮ Equivariant cd-structures and descent theory ⋮ Arithmetic homology and an integral version of Kato's conjecture ⋮ Motivic cohomology: applications and conjectures ⋮ On the vanishing of negative \(K\)-groups ⋮ The Weil-étale topology for number rings ⋮ Weil-étale cohomology and zeta-values of proper regular arithmetic schemes ⋮ The affine part of the Picard scheme ⋮ Witt differentials in the h-topology ⋮ Points in algebraic geometry

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Motivic cohomology over Dedekind rings
• Weil-étale cohomology over finite fields
• La conjecture de Gersten pour les faisceaux de Hodge-Witt logarithmique. (The Gersten conjecture for the logarithmic Hodge-Witt sheaves)
• Continuous étale cohomology
• Mixed motives and algebraic K-theory. (Almost unchanged version of the author's habilitation at Univ. Regensburg 1988)
• Smoothness, semi-stability and alterations
• Tate's conjecture, algebraic cycles and rational \(K\)-theory in characteristic \(p\)
• The negative K-theory of normal surfaces.
• Some finiteness results for étale cohomology.
• Singular homology of abstract algebraic varieties
• The \(K\)-theory of fields in characteristic \(p\)
• Seminar of algebraic geometry du Bois-Marie 1963--1964. Topos theory and étale cohomology of schemes (SGA 4). Vol. 1: Topos theory. Exp. I--IV
• Resolution of singularities of an algebraic variety over a field of characteristic zero. I
• Values of Zeta Functions of Varieties Over Finite Fields
• Équivalences rationnelle et numérique sur certaines variétés de type abélien sur un corps fini
• The Weil-étale topology on schemes over finite fields
• Classes de Chern et classes de cycles en cohomologie de Hodge-Witt logarithmique
• On the De Rham cohomology of algebraic varieties