愛知数論セミナー

第二講演： 15:45 〜 16:45

講演者： Joseph Muller 氏  (東京大学大学院数理科学研究科)

講演題目：Nearby cycles of the PEL GU(1,n-1) Shimura variety over a ramified prime

講演概要：Shimura varieties associated to groups of unitary similitudes have a classical description as moduli spaces of polarized abelian varieties with extra structures. In the case of signature (1,n-1), Pappas built a flat integral model of this Shimura variety over primes which ramify in the reflex field. This model has isolated singularities located inside the special fiber. In this talk, I will explain how to compute the cohomology sheaves of the l-adic nearby cycles complex of this integral model. Our computations rely on Krämer's explicit description of the local model and of its blow-up at the singular points. Since the blow-up has semi-stable reduction, the nearby cycles can now be computed by proper base change.