数学研究所

学术报告

杰出访问研究员综合报告会

Speaker: Prof. Anna Cadoret (Sorbonne Université)

Inviter: 郑维喆 研究员

Language: English

Title: Variation of Tannaka group of perverse sheaves over abelian varieties in families

Time&Venue: 2025年4月25日（星期五） 15:00-16:00  & MCM110

Abstract: Given a relative perverse sheaf P (in the sense of Hansen-Scholze) over an abelian scheme A/S over a smooth irreducible variety S, whose restriction to the geometric generic fiber A_\eta is semisimple (in the corresponding Tannakian category), we prove that the loci of all s in S where the connected component of the derived subgroup of the Tannaka group of P restricted to A_s degenerates is not Zariski-dense. This builds on and enhances previous works by Kramer and Weissauer. Applying our result to intersection complexes, and using computations by Javanpeykar-Lehn-Kramer-Maculan, we derive geometric applications. This is a joint work with Haohao Liu.