Local geometrised Rankin-Selberg method for GL(n)
| dc.creator | Lysenko, Sergey | |
| dc.date | 1999-05-05 | |
| dc.date | 2001-08-30 | |
| dc.date.accessioned | 2026-07-07T05:28:58Z | |
| dc.date.available | 2026-07-07T05:28:58Z | |
| dc.description | Following Laumon [10], to a nonramified $\ell$-adic local system $E$ of rank $n$ on a curve $X$ one associates a complex of $\ell$-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. | |
| dc.description | 36 pages, LaTeX2e, new results are added, final version to appear in Duke Mathematical Journal published by Duke University Press | |
| dc.identifier | https://arxiv.org/abs/math/9905033 | |
| dc.identifier | http://arxiv.org/abs/math/9905033 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/78462 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 11R39; 14H60 | |
| dc.title | Local geometrised Rankin-Selberg method for GL(n) | |
| dc.type | text |