The -parity conjecture for abelian varieties over function fields of characteristic

DOI10.1112/S0010437X13007501zbMath1301.11056WikidataQ123164385 ScholiaQ123164385MaRDI QIDQ2877489

Seidai Yasuda, Fabien Trihan

Publication date: 22 August 2014

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

zbMATH Keywords

abelian varietiesSelmer groupsparity conjectureArtin-Tate conjecture

Mathematics Subject Classification ID

Curves over finite and local fields (11G20) (L)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture (11G40)

Related Items (4)

Selmer groups for elliptic curves in \(\mathbb Z_l^d \)-extensions of function fields of characteristic \(p\) ⋮ The ℓ-parity conjecture over the constant quadratic extension ⋮ On the \(\mu\)-invariants of abelian varieties over function fields of positive characteristic ⋮ Positivity of Hodge bundles of abelian varieties over some function fields

Cites Work

• Some consequences of a formula of Mazur and Rubin for arithmetic local constants
• Regulator constants and the parity conjecture
• On the Birch-Swinnerton-Dyer quotients modulo squares
• The symmetric structure of the plus/minus Selmer groups of elliptic curves over totally real fields and the parity conjecture
• La conjecture de Weil. II
• \(L\)-functions associated to overconvergent \(F\)-isocrystals
• On the conjectures of Birch and Swinnerton-Dyer in characteristic \(p>0\)
• Drinfeld shtukas and Langlands correspondence.
• On the Brauer group of a surface
• Zur Vermutung von Birch und Swinnerton-Dyer über globalen Funktionenkoerpern
• Some consequences of the Riemann hypothesis for varieties over finite fields
• Parity of ranks for elliptic curves with a cyclic isogeny
• On the parity of ranks of Selmer groups II
• Root numbers and parity of ranks of elliptic curves
• Fourier transforms and $p$-adic ‘Weil II’
• The parity conjecture for elliptic curves at supersingular reduction primes
• Root numbers, Selmer groups, and non-commutative Iwasawa theory
• On the parity of ranks of Selmer groups IV. With an appendix by Jean-Pierre Wintenberger
• Finiteness theorems for the cohomology of an overconvergent isocrystal on a curve
• Image directe supérieure et unipotence
• Parity conjectures for elliptic curves over global fields of positive characteristic
• The first de Rham cohomology group and Dieudonné modules

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