题目：Strongly Hodge-Tate implies de Rham

报告人：王宇鹏 复旦大学

时间：2025年12月11日（星期四）10:30-11:30

地点：第五教学楼5505

摘要：Let K be a cdvf of mixed characteristic (0,p) with perfect residue field, G_K be its absolute Galois group, and C be its complete algebraic closure. Let V be a B_dR-representation of G_K. It is easy to see that if V is de Rham, then for any B_dR^+-lattice L of V, L/tL, as a C-representation of G_K, is Hodge-Tate. A suprising theorem of Fontaine tells us the converse is also true：If for any B_dR^+-lattice L of V, L/tL is Hodge--Tate (such a V is called strongly Hodge-Tate)，then V is de Rham. The original proof of Fontaine is quite complicated: He proved this by classifying all C-representations and B_dR-representations of G_K. In my talk, I will provide a new proof of Fontaine's theorem and generalize it to the higher dimension case. Joint with Hui Gao.