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arXiv · 2005.13472

Finiteness of logarithmic crystalline representations

Raju Krishnamoorthy·Jinbang Yang·Kang Zuo
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Abstract

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.

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Raju Krishnamoorthy, Jinbang Yang, Kang Zuo. 2020-05-27. Finiteness of logarithmic crystalline representations. https://arxiv.org/abs/2005.13472

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