The Weil-étale topology for number rings

DOI10.4007/annals.2009.170.657zbMath1278.14029arXivmath/0503604OpenAlexW1999890953MaRDI QIDQ731195

Stephen Lichtenbaum

Publication date: 2 October 2009

Published in: Annals of Mathematics. Second Series (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0503604

zbMATH Keywords

zeta-functionétale cohomologyWeil group

Mathematics Subject Classification ID

Étale and other Grothendieck topologies and (co)homologies (14F20) Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) (14G10) Applications to coding theory and cryptography of arithmetic geometry (14G50) Galois cohomology (11R34)

Related Items (20)

Continuity properties of measurable group cohomology ⋮ Integral motives and special values of zeta functions ⋮ Weil-étale cohomology of curves over \(p\)-adic fields ⋮ The Weil-étale fundamental group of a number field. II ⋮ Cohomology of the Weil group of a \(p\)-adic field ⋮ Двойственность в абелевых многообразиях и формальных группах над локальными полями ⋮ Orthogonal root numbers of tempered parameters ⋮ Tori over number fields and special values at \(s = 1\) ⋮ On the torsion in the cohomology of arithmetic hyperbolic 3-manifolds ⋮ On the analogy between Deninger dynamical systems and the Weil-étale topos ⋮ Zeta functions of regular arithmetic schemes at \(s=0\) ⋮ Hodge correlators ⋮ On cohomology theory for topological groups ⋮ Weil-étale cohomology over finite fields ⋮ Étale cohomology of arithmetic schemes and zeta values of arithmetic surfaces ⋮ Weil-étale cohomology and zeta-values of proper regular arithmetic schemes ⋮ On the Weil-étale cohomology of number fields ⋮ A cocycle model for topological and Lie group cohomology ⋮ A note on the cohomology of the Langlands group ⋮ Special values of \(L\)-functions on regular arithmetic schemes of dimension 1

Cites Work

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• Weil-étale cohomology over finite fields
• Arithmetic cohomology over finite fields and special values of \(\zeta\)-functions
• Local Cross Sections in Locally Compact Groups
• Cohomology of topological groups with applications to the Weil group
• Group Extensions and Cohomology for Locally Compact Groups. III
• On the vanishing of the measurable Schur cohomology groups of Weil groups
• The Weil-étale topology on schemes over finite fields
• Whitehead torsion
• Algebraic Cohomology of Topological Groups

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