Periods of Hilbert modular surfaces

zbMath0489.14014MaRDI QIDQ5905152

Takayuki Oda

Publication date: 1982

Published in: Progress in Mathematics (Search for Journal in Brave)

zbMATH Keywords

Hilbert modular formsHodge structuresHilbert modular varietyelliptic modular formsDoi- Naganuma liftingelliptic curves over arbitrary totally real fieldsisogeny classes of Abelian varietiesOda's main conjecturesplitting of cohomology

Mathematics Subject Classification ID

Research exposition (monographs, survey articles) pertaining to number theory (11-02) Period matrices, variation of Hodge structure; degenerations (32G20) Special values of automorphic (L)-series, periods of automorphic forms, cohomology, modular symbols (11F67) Research exposition (monographs, survey articles) pertaining to algebraic geometry (14-02) Families, moduli, classification: algebraic theory (14J10) Arithmetic ground fields for surfaces or higher-dimensional varieties (14J20) Arithmetic ground fields for abelian varieties (14K15) Transcendental methods, Hodge theory (algebro-geometric aspects) (14C30) Global ground fields in algebraic geometry (14G25) Automorphic forms on (mbox{GL}(2)); Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces (11F41) Langlands-Weil conjectures, nonabelian class field theory (11R39) Special surfaces (14J25) Applications of methods of algebraic (K)-theory in algebraic geometry (14C35) Arithmetic problems in algebraic geometry; Diophantine geometry (14G99)

Related Items (22)

Die Tate-Vermutungen für Hilbert-Blumenthal-Flächen. (The Tate conjectures for Hilbert-Blumenthal surfaces) ⋮ Correspondence of modular forms to cycles associated to \(Sp(p,q)\) ⋮ Motives over totally real fields and \(p\)-adic \(L\)-functions ⋮ Period relations and the Tate conjecture for Hilbert modular surfaces ⋮ Whittaker functions for the large discrete series representations of \(\mathrm{SU}(2,1)\) and related zeta integrals ⋮ Nonvanishing of \(L\)-functions for \(\mathrm{GL}(2)\) ⋮ Darmon points on elliptic curves over number fields of arbitrary signature ⋮ Hilbert Modular Surfaces with p_g ≤ 1 ⋮ Représentation de Weil et changement de base quadratique dans le cas archimédien. II ⋮ Hodge classes and the Jacquet–Langlands correspondence ⋮ Tate cycles on a product of two Hilbert modular surfaces ⋮ Computing Hilbert Modular Forms over Fields with Nontrivial Class Group ⋮ An automorphic approach to Darmon points ⋮ Almost totally complex points on elliptic curves ⋮ Periods of Modular GL₂-type Abelian Varieties and p-adic Integration ⋮ On mixed Hodge structures of Shimura varieties attached to inner forms of the symplectic group of degree two ⋮ Zero-cycles on Hilbert-Blumenthal surfaces ⋮ Theta functions defined by geodesic cycles in quotients of SU(p,1) ⋮ Finite descent obstruction for Hilbert modular varieties ⋮ Overview of the Work of Kumar Murty ⋮ Boundary cohomology of Shimura varieties. II: Hodge theory at the boundary ⋮ Examples of abelian surfaces with everywhere good reduction

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