An algebraic Sato-Tate group and Sato-Tate conjecture

DOI10.1512/iumj.2015.64.5438zbMath1392.11041arXiv1109.4449OpenAlexW2962945237WikidataQ123186467 ScholiaQ123186467MaRDI QIDQ5248696

Kiran S. Kedlaya, Grzegorz Banaszak

Publication date: 8 May 2015

Published in: Indiana University Mathematics Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1109.4449

zbMATH Keywords

Mumford-Tate groupalgebraic Sato-Tate groupnormalized \(L\)-factors

Mathematics Subject Classification ID

Abelian varieties of dimension (> 1) (11G10) Galois representations (11F80) (L)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture (11G40) Global ground fields in algebraic geometry (14G25)

Related Items (15)

Sato–Tate groups of abelian threefolds: a preview of the classification ⋮ On a local-global principle for quadratic twists of abelian varieties ⋮ Sato-Tate distributions of Catalan curves ⋮ Sato-Tate distributions ⋮ Endomorphism fields of abelian varieties ⋮ Arithmetic invariants from Sato-Tate moments ⋮ The twisting Sato-Tate group of the curve \(y^2 = x^{8} - 14x^4 + 1\) ⋮ Sato-Tate distributions of twists of the Fermat and the Klein quartics ⋮ The Tate module of a simple abelian variety of type IV ⋮ Sato-Tate distributions of \(y^2=x^p-1\) and \(y^2=x^{2p}-1\) ⋮ The Sato-Tate conjecture and Nagao's conjecture ⋮ Comparing Hecke coefficients of automorphic representations ⋮ The Mumford-Tate conjecture implies the algebraic Sato-Tate conjecture of Banaszak and Kedlaya ⋮ On the Sato-Tate conjecture for non-generic abelian surfaces ⋮ Tate module tensor decompositions and the Sato-Tate conjecture for certain abelian varieties potentially of \(\mathrm{GL}_2\)-type

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