Motivic \(L\)-functions and Galois module structures

DOI10.1007/BF01444212zbMath0867.11081OpenAlexW2034420302MaRDI QIDQ1914733

Matthias Flach, David J. Burns

Publication date: 9 July 1996

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/165434

zbMATH Keywords

cohomology groupsTate motivesGalois module theoryChinburg invariantsconjecture of Chinburgvalue of motivic \(L\)-functions at zero

Mathematics Subject Classification ID

Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) (14G10) (L)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture (11G40) Integral representations related to algebraic numbers; Galois module structure of rings of integers (11R33)

Related Items

Numerical evidence for the equivariant Birch and Swinnerton-Dyer conjecture (Part II) ⋮ Les nombres de Tamagawa locaux et la conjecture de Bloch et Kato pour les motifs sur un corps abélien ⋮ On Mordell-Weil groups and congruences between derivatives of twisted Hasse-Weil \(L\)-functions ⋮ ON THE GALOIS STRUCTURE OF ARITHMETIC COHOMOLOGY I: COMPACTLY SUPPORTED -ADIC COHOMOLOGY ⋮ Congruences for critical values of higher derivatives of twisted Hasse-Weil \(L\)-functions ⋮ Numerical Evidence for the Equivariant Birch and Swinnerton-Dyer Conjecture ⋮ \(p\)-adic properties of motivic fundamental lines ⋮ Annihilating wild kernels ⋮ On the \(p\)-adic Beilinson conjecture and the equivariant Tamagawa number conjecture ⋮ The universal \(p\)-adic Gross-Zagier formula ⋮ On Extra Zeros of p-Adic L-Functions: The Crystalline Case

Cites Work

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• On certain types of \(p\)-adic representations of the Galois group of a local field; construction of a Barsott-Tate ring.
• On the Galois structure of algebraic integers and S-units
• Exact sequences and Galois module structure
• The root number class and Chinburg's second invariant
• Iwasawa theory and \(p\)-adic Hodge theory
• Cohomology of crystalline representations
• L-values at zero and multiplicative Galois module structure (also Galois Gauss sums and additive Galois module structure).
• A generalisation of the Cassel-Tate pairing.
• Étale $K$-theory and arithmetic
• The projectivity of the moduli space of stable curves. I: Preliminaries on "det" and "Div".
• On Galois structure invariants associated to Tate motives
• On Multiplicative Galois Structure Invariants