LOCAL GEOMETRIZED RANKIN-SELBERG METHOD FOR GL ( n )

@inproceedings{Lysenko2002LOCALGR,
  title={LOCAL GEOMETRIZED RANKIN-SELBERG METHOD FOR GL ( n )},
  author={Sergey I Lysenko},
  year={2002}
}
Following G. Laumon [ 12], to a nonramified̀ -adic local system E of rank n on a curve X one associates a complex of `-adic sheavesnKE 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 productnKE1⊗nKE2 in terms of cohomology of the symmetric powers of X. This may be… CONTINUE READING

From This Paper

Topics from this paper.

References

Publications referenced by this paper.
Showing 1-10 of 11 references

GAITSGORY, Geometric Eisenstein series

D. A. BRAVERMAN
1209
View 11 Excerpts
Highly Influenced

Applications de la formule des traces aux sommes trigonométriques” in Cohomologie étale

P. DELIGNE
Séminaire de Géométrie Algébrique du Bois-Marie (SGA 4 1/2), Lecture Notes in Math. 569, Springer, Berlin • 1977
View 7 Excerpts
Highly Influenced

Euler subgroups” inLie Groups and Their Representations (Budapest

I. I. PIATETSKI-SHAPIRO
1971) , ed. I. M. Gelfand, Halstead, New York • 1975
View 3 Excerpts
Highly Influenced

D

E. FRENKEL
GAITSGORY,andK. VILONEN, Whittaker patterns in the geometry of moduli spaces of bundles on curves , Ann. of Math. (2)153 • 2001

Polo

B. C. NGÔandP
Résolutions de Demazure affines et formule de Casselman-Shalika géométrique , J. Algebraic Geom. 10 • 2001
View 1 Excerpt

Preuve d’une conjecture de Frenkel-Gaitsgory-Kazhdan-Vilonen pour les groupes linéaires généraux

NGÔ B.C.
Israel J. Math. 120 • 2000
View 1 Excerpt

Local geometrized Rankin-Selberg method for GL(n) and its application

S. LYSENKO
C. R. Acad. Sci. Paris Sér. I Math. 329 • 1999

Correspondance de Langlands géométrique pour les corps de fonctions

G. LAUMON
Duke Math. J.54 • 1987
View 1 Excerpt

Two-dimensional̀ -adic representations of the fundamental group of a curve over a finite field and automorphic forms on GL(2)

V. DRINFELD
Amer. J. Math.105 • 1983
View 1 Excerpt

Mumford

F. KNUDSENandD
The projectivity of the moduli space of stable curves, I: Preliminaries on “det” and “Div” , Math. Scand. 39 • 1976
View 1 Excerpt

Similar Papers

Loading similar papers…