Finiteness of logarithmic crystalline representations II

2020/08/31 by Raju Krishnamoorthy, Jinbang Yang, Krishnamoorthy, Raju +3
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2009.00074

openalex publication_date 2020/08/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 π₁(X _K)→ GL_r(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.

Citations

• Deformation theory of periodic Higgs-de Rham flows

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