论文标题
对数晶体表示的有限性ii
Finiteness of logarithmic crystalline representations II
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 $的整数环。让$（x，s）/w $与简单的正常交叉分隔线一起使用，并修复正整数$ r $和$ f $。我们表明，绝对不可约的表示$π_1（x _ {\ bar k}）\ rightArrow \ rightArrow \ mathrm {gl} _r（\ Mathbb {z} _ {p^f}）$来自log crystalline $ \ mathbb z_________________ $（$ fin）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 simple normal crossings divisor and fix positive integers $r$ and $f$. We show that the set of absolutely irreducible representations $π_1(X_{\bar K})\rightarrow \mathrm{GL}_r(\mathbb{Z}_{p^f})$ that come from log crystalline $\mathbb Z_{p^f}$-local systems over $(X_K,S_K)$ of rank $r$ is finite. The proof uses $p$-adic nonabelian Hodge theory and a finiteness result due Abe/Lafforgue.
