Functiones et Approximatio Commentarii Mathematici

Tate conjecture for some abelian surfaces over totally real or CM number fields

Cristian Virdol

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Abstract

In this paper we prove Tate conjecture for abelian surfaces of the type $\operatorname{Res}_{K/F}E$ where $E$ is an elliptic curve defined over a totally real or CM number field $K$, and $F$ is a subfield of $K$ such that $[K:F]=2$.

Article information

Source
Funct. Approx. Comment. Math., Volume 52, Number 1 (2015), 57-63.

Dates
First available in Project Euclid: 20 March 2015

Permanent link to this document
https://projecteuclid.org/euclid.facm/1426857034

Digital Object Identifier
doi:10.7169/facm/2015.52.1.4

Mathematical Reviews number (MathSciNet)
MR3326123

Zentralblatt MATH identifier
1381.11041

Subjects
Primary: 11F41: Automorphic forms on GL(2); Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces [See also 14J20]
Secondary: 11F80: Galois representations 11R42: Zeta functions and $L$-functions of number fields [See also 11M41, 19F27] 11R80: Totally real fields [See also 12J15]

Keywords
Tate conjecture abelian surfaces totally real fields

Citation

Virdol, Cristian. Tate conjecture for some abelian surfaces over totally real or CM number fields. Funct. Approx. Comment. Math. 52 (2015), no. 1, 57--63. doi:10.7169/facm/2015.52.1.4. https://projecteuclid.org/euclid.facm/1426857034


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