Article Dans Une Revue Duke Mathematical Journal Année : 2002

Local geometrized Rankin-Selberg method for GL_n

Résumé

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 $_n{\cal K}_E$ 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 $_n{\cal K}_{E_1}\otimes {_n{\cal K}_{E_2}}$ 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 GL(n) in the framework of the geometric Langlands program.

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Dates et versions

hal-00136936 , version 1 (15-03-2007)

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  • HAL Id : hal-00136936 , version 1

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Sergey Lysenko. Local geometrized Rankin-Selberg method for GL_n. Duke Mathematical Journal, 2002, 111, no. 3, pp.451--493. ⟨hal-00136936⟩
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