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    Caraiani, Ana and Scholze, Peter 2017. On the generic part of the cohomology of compact unitary Shimura varieties. Annals of Mathematics, Vol. 186, Issue. 3, p. 649.
    Johansson, Christian 2016. A trace formula approach to control theorems for overconvergent automorphic forms. manuscripta mathematica, Vol. 151, Issue. 1-2, p. 19.
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A stable trace formula for Igusa varieties

  • Sug Woo Shin (a1)
Abstract

Igusa varieties are smooth varieties in positive characteristic p which are closely related to Shimura varieties and Rapoport–Zink spaces. One motivation for studying Igusa varieties is to analyse the representations in the cohomology of Shimura varieties which may be ramified at p. The main purpose of this work is to stabilize the trace formula for the cohomology of Igusa varieties arising from a PEL datum of type (A) or (C). Our proof is unconditional thanks to the recent proof of the fundamental lemma by Ngô, Waldspurger and many others.

An earlier work of Kottwitz, which inspired our work and proves the stable trace formula for the special fibres of PEL Shimura varieties with good reduction, provides an explicit way to stabilize terms at ∞. Stabilization away from p and ∞ is carried out by the usual Langlands–Shelstad transfer as in work of Kottwitz. The key point of our work is to develop an explicit method to handle the orbital integrals at p. Our approach has the technical advantage that we do not need to deal with twisted orbital integrals or the twisted fundamental lemma.

One application of our formula, among others, is the computation of the arithmetic cohomology of some compact PEL-type Shimura varieties of type (A) with non-trivial endoscopy. This is worked out in a preprint of the author's entitled ‘Galois representations arising from some compact Shimura varieties’.

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COPYRIGHT: © Cambridge University Press 2010
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