Cohomologie d'intersection et fonctions $L$ de certaines variétés de Shimura

DOI10.24033/asens.1476zbMath0553.12005OpenAlexW2407964437MaRDI QIDQ3346418

Jean-Luc Brylinski, Jean-Pierre Labesse

Publication date: 1984

Published in: Annales scientifiques de l'École normale supérieure (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=ASENS_1984_4_17_3_361_0

zbMATH Keywords

Shimura varietiesSelberg trace formulaintersection cohomologyHilbert modular surfaceRamanujan conjecturel-adic cohomologyLefschetz trace formula\(L_ 2\)-cohomologyLanglands conjecture

Mathematics Subject Classification ID

Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) (14G10) Special values of automorphic (L)-series, periods of automorphic forms, cohomology, modular symbols (11F67) Arithmetic aspects of modular and Shimura varieties (11G18) (L)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture (11G40) Representation-theoretic methods; automorphic representations over local and global fields (11F70) Representations of Lie and linear algebraic groups over global fields and adèle rings (22E55) Langlands-Weil conjectures, nonabelian class field theory (11R39)

Related Items (29)

Unnamed Item ⋮ On the zeta functions of Shimura varieties and periods of Hilbert modular forms ⋮ Period relations and the Tate conjecture for Hilbert modular surfaces ⋮ Non-paritious Hilbert modular forms ⋮ Hirzebruch-Zagier cycles and twisted triple product Selmer groups ⋮ EULER SYSTEMS FOR HILBERT MODULAR SURFACES ⋮ On ordinary \(\lambda\)-adic representations associated to modular forms ⋮ Hodge classes and the Jacquet–Langlands correspondence ⋮ Arithmetic distribution of tempered components of cuspidal representations of \(\mathrm{GL}(3)\) ⋮ Non-solvable base change for Hilbert modular representations and zeta functions of twisted quaternionic Shimura varieties ⋮ Supersingular locus of Hilbert modular varieties, arithmetic level raising and Selmer groups ⋮ On Galois representations associated to Hilbert modular forms ⋮ On sums of three squares. ⋮ On norm relations for Asai–Flach classes ⋮ Higher regulators, Hilbert modular surfaces, and special values of \(L\)-functions ⋮ Galois representations modulo p and cohomology of Hilbert modular varieties ⋮ The cyclotomic Iwasawa main conjecture for Hilbert cusp forms with complex multiplication ⋮ Complexes pondérés sur les compactifications de Baily-Borel: Le cas des variétés de Siegel ⋮ On the distribution of Satake parameters of \(\text{GL}_2\) holomorphic cuspidal representations ⋮ Ordinary primes in Hilbert modular varieties ⋮ On Ihara’s lemma for Hilbert modular varieties ⋮ Zero-cycles on Hilbert-Blumenthal surfaces ⋮ Unnamed Item ⋮ Tate cycles on some quaternionic Shimura varieties mod \(p\) ⋮ The Ramanujan conjecture and its applications ⋮ The Ramanujan property for regular cubical complexes ⋮ On Artin L-functions associated to Hilbert modular forms of weight one ⋮ On liftings and cusp cohomology of arithmetic groups ⋮ On the \(l\)-adic cohomology of Siegel threefolds

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