K-theory of semi-linear endomorphisms via the Riemann-Hilbert\n correspondence

2016/10/03 by Oliver Bräunling, Braunling, Oliver
Mathematics · #19F27 #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT) #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1610.00540

openalex publication_date 2016/10/03 · openalex created_date 2022/08/29 · openalex updated_date 2026/07/28

Abstract

Grayson, developing ideas of Quillen, has made computations of the K-theory\nof "semi-linear endomorphisms". In the present text we develop a technique to\ncompute these groups in the case of Frobenius semi-linear actions. The main\nidea is to interpret the semi-linear modules as crystals and use a positive\ncharacteristic version of the Riemann-Hilbert correspondence. We also compute\nthe K-theory of the category of etale constructible p-torsion sheaves.\n

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