Tate classes and poles of \(L\)-functions of twisted quaternionic Shimura surfaces

DOI10.1016/J.JNT.2006.07.003zbMath1174.14021OpenAlexW1972998700MaRDI QIDQ2370185

Cristian Virdol

Publication date: 22 June 2007

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jnt.2006.07.003

zbMATH Keywords

\(L\)-functionsTate conjecturetwisted quaternionic Shimura surfaces

Mathematics Subject Classification ID

Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) (14G10) Arithmetic aspects of modular and Shimura varieties (11G18) (L)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture (11G40) Modular and Shimura varieties (14G35)

Related Items (5)

The critical values of \(L\)-functions of CM-base change for Hilbert modular forms ⋮ Non-solvable base change for Hilbert modular representations and zeta functions of twisted quaternionic Shimura varieties ⋮ Tate classes and \(L\)-functions on a product of a quaternionic Shimura surface and a Picard modular surface ⋮ ON THE SPECIAL VALUES OF L-FUNCTIONS OF CM-BASE CHANGE FOR HILBERT MODULAR FORMS ⋮ The meromorphic continuation of the zeta function of a product of Hilbert and Picard modular surfaces over CM-fields

Cites Work

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• Algebraic cycles on compact Shimura surface
• On Galois representations associated to Hilbert modular forms
• Die Tate-Vermutungen für Hilbert-Blumenthal-Flächen. (The Tate conjectures for Hilbert-Blumenthal surfaces)
• Period relations and the Tate conjecture for Hilbert modular surfaces
• Modularity of the Rankin-Selberg \(L\)-series, and multiplicity one for \(\mathrm{SL}(2)\)
• Tate cycles on a product of two Hilbert modular surfaces
• A relation between automorphic representations of ${\rm GL}(2)$ and ${\rm GL}(3)$

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