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15 February 2002 Local geometrized Rankin-Selberg method for GL(n)
Sergey Lysenko
Duke Math. J. 111(3): 451-493 (15 February 2002). DOI: 10.1215/S0012-7094-02-11133-8

Abstract

Following G. Laumon [12], to a nonramified $\ell$-adic local system $E$ of rank $n$ on a curve $X$ one associates a complex of $\ell$-adic sheaves $\sb n\mathscr {K}\sb E$ on the moduli stack of rank $n$ vector bundles on $X$ with a section, which is cuspidal and satisfies the Hecke property for $E$. This is a geometric counterpart of the well-known construction due to J. Shalika [19] and I. Piatetski-Shapiro [18]. We express the cohomology of the tensor product $\sb n\mathscr {K}\sb {E\sb 1}\otimes \sb n\mathscr {K}\sb {E\sb 2}$ 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 ${\rm GL}(n)$ in the framework of the geometric Langlands program.

Citation

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Sergey Lysenko. "Local geometrized Rankin-Selberg method for GL(n)." Duke Math. J. 111 (3) 451 - 493, 15 February 2002. https://doi.org/10.1215/S0012-7094-02-11133-8

Information

Published: 15 February 2002
First available in Project Euclid: 18 June 2004

zbMATH: 1080.11040
MathSciNet: MR1885828
Digital Object Identifier: 10.1215/S0012-7094-02-11133-8

Subjects:
Primary: 11R39
Secondary: 11F70, 11S37, 14H60, 22E50, 22E55

Rights: Copyright © 2002 Duke University Press

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Vol.111 • No. 3 • 15 February 2002
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