Shimura varieties with Γ 1 ( p ) -level via Hecke algebra isomorphisms: the Drinfeld case

Thomas J. Haines; Michael Rapoport

Annales scientifiques de l'École Normale Supérieure (2012)

  • Volume: 45, Issue: 5, page 719-785
  • ISSN: 0012-9593

Abstract

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We study the local factor at  p of the semi-simple zeta function of a Shimura variety of Drinfeld type for a level structure given at  p by the pro-unipotent radical of an Iwahori subgroup. Our method is an adaptation to this case of the Langlands-Kottwitz counting method. We explicitly determine the corresponding test functions in suitable Hecke algebras, and show their centrality by determining their images under the Hecke algebra isomorphisms of Goldstein, Morris, and Roche.

How to cite

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Haines, Thomas J., and Rapoport, Michael. "Shimura varieties with $\Gamma _1(p)$-level via Hecke algebra isomorphisms: the Drinfeld case." Annales scientifiques de l'École Normale Supérieure 45.5 (2012): 719-785. <http://eudml.org/doc/272197>.

@article{Haines2012,
abstract = {We study the local factor at $p$ of the semi-simple zeta function of a Shimura variety of Drinfeld type for a level structure given at $p$ by the pro-unipotent radical of an Iwahori subgroup. Our method is an adaptation to this case of the Langlands-Kottwitz counting method. We explicitly determine the corresponding test functions in suitable Hecke algebras, and show their centrality by determining their images under the Hecke algebra isomorphisms of Goldstein, Morris, and Roche.},
author = {Haines, Thomas J., Rapoport, Michael},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {Shimura varieties; Hasse-Weil zeta functions; automorphic $L$-functions},
language = {eng},
number = {5},
pages = {719-785},
publisher = {Société mathématique de France},
title = {Shimura varieties with $\Gamma _1(p)$-level via Hecke algebra isomorphisms: the Drinfeld case},
url = {http://eudml.org/doc/272197},
volume = {45},
year = {2012},
}

TY - JOUR
AU - Haines, Thomas J.
AU - Rapoport, Michael
TI - Shimura varieties with $\Gamma _1(p)$-level via Hecke algebra isomorphisms: the Drinfeld case
JO - Annales scientifiques de l'École Normale Supérieure
PY - 2012
PB - Société mathématique de France
VL - 45
IS - 5
SP - 719
EP - 785
AB - We study the local factor at $p$ of the semi-simple zeta function of a Shimura variety of Drinfeld type for a level structure given at $p$ by the pro-unipotent radical of an Iwahori subgroup. Our method is an adaptation to this case of the Langlands-Kottwitz counting method. We explicitly determine the corresponding test functions in suitable Hecke algebras, and show their centrality by determining their images under the Hecke algebra isomorphisms of Goldstein, Morris, and Roche.
LA - eng
KW - Shimura varieties; Hasse-Weil zeta functions; automorphic $L$-functions
UR - http://eudml.org/doc/272197
ER -

References

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