1999/05/05 by Sergey Lysenko, Lysenko, Sergey
Mathematics · #11R39 #14H60 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research #math.AG #msc:11R39 #msc:14H60
paper · pdf · doi:10.48550/arxiv.math/9905033
36 pages, LaTeX2e, new results are added, final version to appear in Duke Mathematical Journal published by Duke University Press
openalex publication_date 1999/05/05 · arxiv created 2001/08/30 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Following Laumon [10], to a nonramified ℓ-adic local system E of rank n on a curve X one associates a complex of ℓ-adic sheaves n\cal KE on the moduli stack of rank n vector bundles on X with a section, which is cuspidal and satisfies Hecke property for E. This is a geometric counterpart of the well-known construction due to Shalika [17] and Piatetski-Shapiro [16]. We express the cohomology of the tensor product n\cal KE1⊗ n\cal KE2 in terms of cohomology of the symmetric powers of X. This may be considered as a geometric interpretation of the local part of the classical Rankin-Selberg method for GL(n) in the framework of the geometric Langlands program.