Hodge and Mumford-Tate groups of an abelian variety, complex multiplication, and Frobenius elements

DOI10.1134/S0001434623030331MaRDI QIDQ2699802

S. G. Tankeev

Publication date: 19 April 2023

Published in: Mathematical Notes (Search for Journal in Brave)

zbMATH Keywords

abelian varietycomplex multiplicationFrobeniusHodge and Mumford-Tate groups

Mathematics Subject Classification ID

Complex multiplication and moduli of abelian varieties (11G15) Variation of Hodge structures (algebro-geometric aspects) (14D07) Transcendental methods, Hodge theory (algebro-geometric aspects) (14C30)

Cites Work

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• Hodge cycles, motives, and Shimura varieties
• Endomorphisms of Abelian varieties over finite fields
• A note of Shimura's paper: Discontinuous groups and Abelian varieties
• Good reduction of abelian varieties
• \(L\)-functions of number fields and zeta functions of abelian varieties
• ℓ-Adic and λ-Adic Representations Associated to Abelian Varieties Defined Over Number Fields
• Examples of genus two CM curves defined over the rationals
• A Survey of the Hodge Conjecture
• INTERRELATIONS BETWEEN THE TATE AND HODGE CONJECTURES FOR ABELIAN VARIETIES

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