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Seminar

Number Theory Seminar: On some Tate cycles on Shimura varieties October 22, 2014 (03:40 PM PDT - 05:00 PM PDT)
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Location: 740 Evans Hall
Speaker(s) Xinwen Zhu (California Institute of Technology)
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This is based on a joint work with Liang Xiao. I will first describe certain conjectural Tate classes in the middle dimensional etale cohomology of many Shimura varieties over finite fields (starting from Hilbert and Picard modular surfaces at inert primes). According to the Tate conjecture, there should exist corresponding algebraic cycles. Surprisingly, we find that these cycles are provided by the supersingular (or more precisely basic) loci of these Shimura varieties. I will explain how to understand the situation using the geometric Satake in mixed characteristic.

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