论文标题
对数结晶表示的有限性
Finiteness of logarithmic crystalline representations
论文作者
论文摘要
让$ k $是一个未经塑造的$ p $ - 亚种本地领域，让$ w $是$ k $的整数环。令$（x，s）/w $与正常的交叉分隔线一起是一个平稳的适当方案。我们表明，只有许多日志晶体$ \ mathbb z_ {p^f} $ - $ x_k \ setminus s_k $的本地系统的给定等级的s_k $，并且具有绝对不可约的残留表示，直至由角色扭曲。该证明使用$ p $ - 美国的非亚伯杂货理论，并且由于Abe/lafforgue而成为有限的结果。
Let $K$ be an unramified $p$-adic local field and let $W$ be the ring of integers of $K$. Let $(X,S)/W$ be a smooth proper scheme together with a normal crossings divisor. We show that there are only finitely many log crystalline $\mathbb Z_{p^f}$-local systems over $X_K\setminus S_K$ of given rank and with geometrically absolutely irreducible residual representation, up to twisting by a character. The proof uses $p$-adic nonabelian Hodge theory and a finiteness result due Abe/Lafforgue.
