Period relations and the Tate conjecture for Hilbert modular surfaces

DOI10.1007/BF01389081zbMath0631.14005WikidataQ102398538 ScholiaQ102398538MaRDI QIDQ1094479

Dinakar Ramakrishnan, V. Kumar Murty

Publication date: 1987

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

Full work available at URL: https://eudml.org/doc/143483

zbMATH Keywords

Picard groupHilbert modular surfacesHodge cyclesCM-motivesHilbert modular forms of CM-typeTate conjecture for algebraic cycles

Mathematics Subject Classification ID

Picard groups (14C22) 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) Generalizations (algebraic spaces, stacks) (14A20) Cycles and subschemes (14C99)

Related Items

Otto Blumenthal (1876--1944) in retrospect, Die Tate-Vermutungen für Hilbert-Blumenthal-Flächen. (The Tate conjectures for Hilbert-Blumenthal surfaces), Tate classes and poles of \(L\)-functions of twisted quaternionic Shimura surfaces, Hodge classes and the Jacquet–Langlands correspondence, 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, Open problems on central simple algebras., ALGEBRAIC CYCLES AND TATE CLASSES ON HILBERT MODULAR VARIETIES, 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 \(p\), Tate conjecture for some abelian surfaces over totally real or CM number fields, Overview of the Work of Kumar Murty

Cites Work

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