《北京数学杂志》学术会议5月17日邀请报告——De Rham Comparison for Boundary Cohomology
报告人：蓝凯文 (University of Minnesota Twin Cities)
时间：2024-05-17 16:20-17:20
地点：304am永利集团镜春园82号甲乙丙楼报告厅
报告摘要：Let $X$ be any variety smooth but not necessarily proper over the $p$-adic numbers. In joint works with Hansheng Diao, Ruochuan Liu, and Xinwen Zhu, we constructed a Riemann-Hilbert functor sending any $p$-adic etale local system $L$ over $X$ to a regular integrable connection $RH(L)$ over $X$, and we showed that, when $L$ is de Rham, we have a comparison isomorphism between the etale cohomology of $L$ and the de Rham cohomology of $RH(L)$ after tensoring with Fontaine's period ring $B_{dR}$. In joint work with Ruochuan Liu and Xinwen Zhu that is published in the Peking Mathematical Journal, we also established compatible analogues for the compactly supported cohomology and the so-called interior cohomology. In this talk, I will explain yet another analogue for the so-called boundary cohomology, which naturally complements the interior cohomology, and some further generalizations, based on joint work with David Sherman. I will start with a general review, and explain our strategy. If time permits, I will also explain some applications to Shimura varieties.
