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arXiv · 2009.00074

Finiteness of logarithmic crystalline representations II

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 simple normal crossings divisor and fix positive integers $r$ and $f$. We show that the set of absolutely irreducible representations $\pi_1(X_{\bar K})\rightarrow \mathrm{GL}_r(\mathbb{Z}_{p^f})$ 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.

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Raju Krishnamoorthy, Jinbang Yang, Kang Zuo. 2020-08-31. Finiteness of logarithmic crystalline representations II. https://arxiv.org/abs/2009.00074

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