中科院数学与系统科学研究院
数学研究所
数论研讨班
告人： Shen-Ning Tung（University Duisburg-Essen）
题 目：On the finiteness of patched completed cohomology
时 间：2019.07.02（星期二），15:30-16:30
地 点：晨兴110室
摘 要：We prove that after applying the generalized Colmez functor constructed by Zábrádi, the patched completed cohomology with an action of \prod^r_{i=1} GL_2(Q_p) is finite over the patched Galois deformation ring. This result has the following two applications. First of all, it gives a new proof of the Breuil-Mézard conjecture for 2-dimensional representations of the absolute Galois group of Q_p, which is new in the case p = 2 or 3 and \overline{r} a twist of an extension of the trivial character by the mod p cyclotomic character. As a consequence, a local restriction in the proof of Fontaine-Mazur conjecture by Kisin, Hu-Tan and Paskunas is removed. Secondly, it gives another proof of the 'big R = big T' theorem of Gee-Newton without the formally smoothness assumption at p.
