题目：p-adic monodromy groups of supersingular abelian surfaces over \mathbb{Q}_p

报告人：陈陌青 斯特拉斯堡大学

时间：2025年6月2日10：00

地点：东区第五教学楼5307教室

摘要：For any proper smooth variety over a p-adic field with good reduction, its p-adic étale cohomology gives rise to a crystalline Galois representation, which can be studied via linear algebraic structures in p-adic Hodge theory. The monodromy group—defined as the Zariski closure of the image of such a representation—is typically quite mysterious. Recently, we focus on abelian surfaces over \mathbb{Q}_p with good reduction whose special fibers are supersingular, which we refer to as supersingular abelian surfaces over \mathbb{Q}_p. We determine the possible p-adic monodromy groups arising from such abelian surfaces using tools from p-adic Hodge theory and Tannakian formalism. In this talk, I’ll introduce Fontaine’s mysterious functor and explain how it helps the computation of p-adic monodromy groups. We’ll also discuss the connection with the p-adic period mapping.