Higher regulators, Hilbert modular surfaces, and special values of \(L\)-functions

DOI10.1215/S0012-7094-98-09202-XzbMath0962.11024OpenAlexW2027883985MaRDI QIDQ1974792

Guido Kings

Publication date: 27 March 2000

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1215/s0012-7094-98-09202-x

zbMATH Keywords

motivic cohomologyHilbert modular surfaceabsolute Hodge cohomologyhigher regulators

Mathematics Subject Classification ID

Special values of automorphic (L)-series, periods of automorphic forms, cohomology, modular symbols (11F67) Arithmetic aspects of modular and Shimura varieties (11G18) Modular and Shimura varieties (14G35) Automorphic forms on (mbox{GL}(2)); Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces (11F41) Étale cohomology, higher regulators, zeta and (L)-functions ((K)-theoretic aspects) (19F27)

Related Items

Gross-Prasad periods for reducible representations, EULER SYSTEMS FOR HILBERT MODULAR SURFACES, Euler systems and the Bloch-Kato conjecture for automorphic Galois representations, On a local-global principle for quadratic twists of abelian varieties, Norm-compatible systems of Galois cohomology classes for \(\mathrm{GSp}_6\), The Bloch-Kato conjecture on special values of \(L\)-functions. A survey of known results., On higher regulators of Siegel threefolds II: the connection to the special value, Standard conjectures for abelian fourfolds, TWISTED TRIPLE PRODUCT -ADIC L-FUNCTIONS AND HIRZEBRUCH–ZAGIER CYCLES, Motivic hyper-Kähler resolution conjecture. I: Generalized Kummer varieties, Higher regulators, periods and special values of the degree 4 \(L\)-function of \(\text{GSp}(4)\), Decomposition of abelian motives, Syntomic regulators of Asai-Flach classes, The motive of a smooth theta divisor, Functoriality of motivic lifts of the canonical construction

Cites Work

• Regularization theorems in Lie algebra cohomology. Applications
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• Motives for Hilbert modular forms
• Appendix to ``The Iwasawa conjecture for totally real fields by A.Wiles: Arithmetic minimal compactification of the Hilbert-Blumenthal moduli spaces
• Motives for modular forms
• Faisceaux amples sur les schémas en groupes et les espaces homogènes
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• Théorie de Hodge. III
• Automorphic forms on \(\mathrm{GL}(2)\). Part II
• Higher regulators and Hecke \(L\)-series of imaginary quadratic fields. I
• Cohomologie d'intersection et fonctions $L$ de certaines variétés de Shimura
• Laplacian and the Discrete Spectrum of an Arithmetic Group
• L-Indistinguishability For SL (2)
• On the Zeta-Functions of Some Simple Shimura Varieties
• Stable real cohomology of arithmetic groups
• Algebraic cycles in families of abelian varieties over Hilbert-Blumenthal surfaces.
• On the critical values of Hecke L-series
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