Hecke correspondence and Betti cohomology groups for smooth compactifications of Hilbert modular varieties of dimension \(\leq 3\)

DOI10.3792/pjaa.72.189zbMath0914.11021OpenAlexW1996589242MaRDI QIDQ676772

Kazuyuki Hatada

Publication date: 20 March 1997

Published in: Proceedings of the Japan Academy. Series A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3792/pjaa.72.189

zbMATH Keywords

eigenvaluesHilbert modular varietiesBetti cohomology groupsrepresentations of Hecke correspondencessmooth toroidal compactifications

Mathematics Subject Classification ID

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) Hecke-Petersson operators, differential operators (several variables) (11F60)

Cites Work

• Correspondences for Hecke rings and (co-)homology groups on smooth compactifications of Siegel modular varieties
• On the action of Hecke rings on homology groups of smooth compactifications of Siegel modular varieties and Siegel cusp forms
• On the local zeta functions of the Hilbert modular schemes
• Intersection numbers of curves on Hilbert modular surfaces and modular forms of Nebentypus
• Hirzebruch's proportionality theorem in the non-compact case
• The special values of the zeta functions associated with Hilbert modular forms
• Correspondences for Hecke rings and \(\ell\)-adic cohomology groups on smooth compactifications of Siegel modular varieties
• Two theorems on modular curves
• Hilbert modular surfaces
• On discontinuous groups operating on the product of the upper half planes
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