Shimura varieties with ${\Gamma }_1(p)$-level via Hecke algebra isomorphisms: the Drinfeld case

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 use Hecke algebra isomorphisms to determine the test functions at p.

71 pages, 1 figure. Some LaTex glitches corrected. Remark 10.2.2 revised to account for a correction in the companion paper [H10]

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