Picard modular forms and the cohomology of local systems on a Picard modular surface

DOI10.4171/CMH/532MaRDI QIDQ2159486

Gerard van der Geer, Jonas Bergström

Publication date: 1 August 2022

Published in: Commentarii Mathematici Helvetici (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2012.07673

zbMATH Keywords

curves over finite fieldsHecke eigenvaluePicard modular surfacePicard modular formHarder conjecture

Mathematics Subject Classification ID

Families, moduli of curves (algebraic) (14H10) Modular and automorphic functions (11F03) Curves over finite and local fields (11G20) Arithmetic aspects of modular and Shimura varieties (11G18) Modular and Shimura varieties (14G35) Moduli, classification: analytic theory; relations with modular forms (14J15)

Cites Work

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• Mixed Hodge complexes and \(L^2\)-cohomology for local systems on ball quotients
• Rank one Eisenstein cohomology of local systems on the moduli space of abelian varieties
• Concomitants of ternary quartics and vector-valued Siegel and Teichmüller modular forms of genus three
• The integral monodromy of hyperelliptic and trielliptic curves
• Eisensteinkohomologie für Gruppen vom Typ \(GU(2,1)\). (Eisenstein cohomology for groups of type \(GU(2,1)\))
• On the Fourier coefficients of automorphic forms at various cusps and some applications to Rankin's convolution
• Hirzebruch's proportionality theorem in the non-compact case
• On certain arithmetic automorphic forms for SU(1,q)
• The arithmetic of automorphic forms with respect to a unitary group
• Eisenstein cohomology and the construction of mixed motives
• Some computational results on Hecke eigenvalues of modular forms on a unitary group
• On the cohomology of local systems on the moduli spaces of curves of genus 2 and of Abelian surfaces. II.
• Motives for modular forms
• On the Eisenstein cohomology of arithmetic groups
• Stable Higgs bundles with trivial Chern classes. Several examples
• Siegel modular forms of degree three and the cohomology of local systems
• On purely transcendental fields of automorphic functions of several variables
• Remarque sur une formule de Shimura-Taniyama
• Generators for modules of vector-valued Picard modular forms
• Congruence Between a Siegel and an Elliptic Modular Form
• On a theorem of Stickelberger
• Vector Bundles Over an Elliptic Curve
• The Euler characteristic of local systems on the moduli of curves and abelian varieties of genus three
• Cohomology of moduli spaces of curves of genus three via point counts
• Über die Anzahl der Spitzen einiger arithmetischer Untergruppen unitärer Gruppen
• Automorphic Representation of Unitary Groups in Three Variables. (AM-123)
• On the First Cohomology of Discrete Subgroups of Semi-Simple Lie Groups

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