Weil-étale cohomology and zeta-values of proper regular arithmetic schemes

DOI10.25537/dm.2018v23.1425-1560zbMath1404.14024arXiv1605.01277MaRDI QIDQ1799379

Matthias Flach, Baptiste Morin

Publication date: 18 October 2018

Published in: Documenta Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1605.01277

zbMATH Keywords

Arakelov theoryWeil-étale cohomologyZeta functionsZeta-values

Mathematics Subject Classification ID

Étale and other Grothendieck topologies and (co)homologies (14F20) (L)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture (11G40) Motivic cohomology; motivic homotopy theory (14F42)

Related Items (11)

SPECIAL VALUES OF THE ZETA FUNCTION OF AN ARITHMETIC SURFACE ⋮ On integral class field theory for varieties over \(p\)-adic fields ⋮ Non-commutative geometry and cyclic homology. Abstracts from the workshop held July 31 -- August 6, 2022 ⋮ PONTRYAGIN DUALITY FOR VARIETIES OVER p-ADIC FIELDS ⋮ SPECIAL VALUES OF ZETA-FUNCTIONS OF REGULAR SCHEMES ⋮ VALUES OF ZETA FUNCTIONS OF ARITHMETIC SURFACES AT ⋮ Tori over number fields and special values at \(s = 1\) ⋮ Algebraic number theory. Abstracts from the workshop held June 25--30, 2023 ⋮ Compatibility of special value conjectures with the functional equation of zeta functions ⋮ Étale cohomology of arithmetic schemes and zeta values of arithmetic surfaces ⋮ Special values of \(L\)-functions on regular arithmetic schemes of dimension 1

Cites Work

• Milne's correcting factor and derived de Rham cohomology
• Syntomic cohomology and \(p\)-adic regulators for varieties over \(p\)-adic fields
• Higher arithmetic Chow groups
• On the Weil-étale topos of regular arithmetic schemes
• Comparison of dualizing complexes
• On the \(p\)-adic local invariant cycle theorem
• Syntomic complexes and \(p\)-adic nearby cycles
• Duality via cycle complexes
• Milne's correcting factor and derived de Rham cohomology. II
• Motivic cohomology over Dedekind rings
• Weil-étale cohomology over finite fields
• The Weil-étale topology for number rings
• Homological algebra with locally compact Abelian groups
• Iwasawa theory of crystalline representations. II.
• Algebraic cycles and higher K-theory
• De Rham cohomology and conductors of curves
• A note on p-adic étale cohomology
• La conjecture de Weil. II
• Arithmetic intersection theory
• Spectral sequence of weights in Hyodo-Kato cohomology
• Arakelov Chow groups of abelian schemes, arithmetic Fourier transform, and analogues of the standard conjectures of Lefschetz type
• Finiteness and cohomological purity in rigid cohomology (with an appendix by Aise Johan de Jong)
• On the equivariant Tamagawa number conjecture for Tate motives
• Bloch-Kato conjecture and Main Conjecture of Iwasawa theory for Dirichlet characters
• Special \(L\)-values of geometric motives
• Resolution of unbounded complexes in Grothendieck categories
• Chow polylogarithms and regulators
• Theory of tubular neighborhood in étale topology
• The \(K\)-theory of fields in characteristic \(p\)
• On the crystalline period map
• \(p\)-adic deformation of algebraic cycle classes
• Zeta functions of regular arithmetic schemes at \(s=0\)
• Logarithmic Hodge-Witt sheaves on normal crossing varieties
• Arithmetic cohomology over finite fields and special values of \(\zeta\)-functions
• Complexe cotangent et déformations. I. (The cotangent complex and deformations. I.)
• Complexe cotangent et déformations. II
• Étale motives
• On the cyclotomic main conjecture for the prime 2
• Polylogarithms, regulators, and Arakelov motivic complexes
• Arakelov motivic cohomology I
• Arakelov motivic cohomology II
• Les Constantes des Equations Fonctionnelles des Fonctions L
• Cohomology of topological groups with applications to the Weil group
• Opérations En K-Théorie Algébrique
• Values of Zeta Functions of Varieties Over Finite Fields
• An Etale Cohomology Duality Theorem for Number Fields with A Real Embedding
• Complexe de de\thinspace Rham-Witt et cohomologie cristalline
• The projectivity of the moduli space of stable curves. I: Preliminaries on "det" and "Div".
• Derived de Rham Complex and Cyclic Homology.
• Équivalences rationnelle et numérique sur certaines variétés de type abélien sur un corps fini
• The Bloch-Kato conjecture and a theorem of Suslin-Voevodsky
• Syntomic cohomology and $p$-adic motivic cohomology
• The Weil-étale topology on schemes over finite fields
• Triangulated Categories of Mixed Motives
• p-adic étale Tate twists and arithmetic duality☆
• The Abel–Jacobi map for higher Chow groups
• Lois polynomes et lois formelles en théorie des modules
• Number theory and dynamical systems on foliated spaces
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Weil-étale cohomology and zeta-values of proper regular arithmetic schemes