Abstract
A recent conjecture of Kottwitz predicts that certain central elements in Iwahori-Hecke algebras play an important role in the bad reduction of Shimura varieties with Iwahori level structure. Namely, the function trace of Frobenius on nearby cycles is conjecturally expressible in terms of the so-called Bernstein function zμ corresponding to the cocharacter μ coming from the Shimura data. In this paper we prove an explicit formula for zμ in terms of the standard basis for the Iwahori-Hecke algebra, for any minuscule cocharacter μ of any p-adic group G. We then use this formula to prove Kottwitz's conjecture for a particular Shimura variety, attached to G=GU(1,d−1) and μ=(1,0d−1), known as the "Drinfeld case."
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.