Tate classes and \(L\)-functions on a product of a quaternionic Shimura surface and a Picard modular surface

DOI10.1016/J.JNT.2007.12.005zbMath1179.11019OpenAlexW2001681230MaRDI QIDQ927697

Cristian Virdol

Publication date: 9 June 2008

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

Full work available at URL: https://doi.org/10.1016/j.jnt.2007.12.005

zbMATH Keywords

Picard modular surfaceTate conjecturequaternionic Shimura surface

Mathematics Subject Classification ID

Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) (14G10) Galois representations (11F80) 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)

Cites Work

• Algebraic cycles on compact Shimura surface
• On Galois representations associated to Hilbert modular forms
• On Artin L-functions associated to Hilbert modular forms of weight one
• 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 classes on a product of two Picard modular surfaces
• Tate cycles on a product of two Hilbert modular surfaces
• Tate classes and poles of \(L\)-functions of twisted quaternionic Shimura surfaces
• Non-solvable base change for Hilbert modular representations and zeta functions of twisted quaternionic Shimura varieties
• Rankin-Selberg Convolutions
• Simple Algebras, Base Change, and the Advanced Theory of the Trace Formula. (AM-120)
• Travaux de Shimura
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