Die Tate-Vermutungen für Hilbert-Blumenthal-Flächen. (The Tate conjectures for Hilbert-Blumenthal surfaces)

DOI10.1007/BF01389080zbMath0601.14007MaRDI QIDQ1080901

Chr. Klingenberg

Publication date: 1987

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/143482

zbMATH Keywords

Tate conjecture on algebraic cyclesHilbert-Blumenthal surfacesinstability of CM automorphic forms

Mathematics Subject Classification ID

Automorphic forms on (mbox{GL}(2)); Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces (11F41) Special surfaces (14J25) Cycles and subschemes (14C99)

Related Items

Otto Blumenthal (1876--1944) in retrospect ⋮ Tate classes and poles of \(L\)-functions of twisted quaternionic Shimura surfaces ⋮ Period relations and the Tate conjecture for Hilbert modular surfaces ⋮ Recent progress on the Tate conjecture ⋮ Tate classes and \(L\)-functions on a product of a quaternionic Shimura surface and a Picard modular surface ⋮ Tate cycles on a product of two Hilbert modular surfaces ⋮ ALGEBRAIC CYCLES ON COMPACT QUATERNIONIC SHIMURA FOURFOLDS AND POLES OF L-FUNCTIONS ⋮ Algebraic cycles on a product of two Hilbert modular surfaces ⋮ A rank inequality for the Tate conjecture over global function fields ⋮ Zero-cycles on Hilbert-Blumenthal surfaces ⋮ Tate cycles on some quaternionic Shimura varieties mod \(p\)

Cites Work

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• Algebraic cycles on compact Shimura surface
• Finiteness theorems for abelian varieties over number fields.
• Period relations and the Tate conjecture for Hilbert modular surfaces
• Hodge cycles, motives, and Shimura varieties
• L-indistinguishability and R groups for the special linear group
• Intersection numbers of curves on Hilbert modular surfaces and modular forms of Nebentypus
• Compactification of arithmetic quotients of bounded symmetric domains
• On the functional equation of certain Dirichlet series
• Automorphic forms on GL (2)
• On canonical models of arithmetic quotients of bounded symmetric domains
• L-Indistinguishability For SL (2)
• Automorphic Forms on Adele Groups. (AM-83)
• Travaux de Shimura
• Periods of Hilbert modular surfaces