This talk studies how p-adic Hodge-theoretic invariants vary in families near rank-1 points of adic spaces. I will begin with joint work with Tong Liu, Yong Suk Moon, and Koji Shimizu establishing a purity theorem for semistable p-adic local systems. I will then outline a geometric approach via vector bundles on the relative Fargues–Fontaine curve. In ongoing work, we investigate how these vector bundles vary in neighborhoods of rank-1 points.

报告人简介：杜衡，博士毕业于普渡大学，现任清华大学数学科学中心助理教授。研究方向为数论，p 进霍奇理论。