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- W2000737868 abstract "We study a positive characteristic analogue of the nonabelian Hodge structure constructed by Katzarkov, Pantev, and Toen on the homotopy type of a complex algebraic variety. Given a proper smooth scheme X over a perfect field of characteristic p and a Tannakian category C of isocrystals on X, we construct an object XC in a suitable homotopy category of simplicial presheaves whose category of local systems is equivalent to C in a manner compatible with cohomology. We then study F-isocrystal structure on these simplicial presheaves. As applications of the theory, we prove a p-adic analogue of a result of Hain on relative Malcev completions, a generalization to the level of homotopy types of a theorem of Katz relating p-adic étale local systems and F-isocrystals, as well as a p-adic version of the formality theorem in homotopy theory. We have also included a new proof based on reduction modulo p of the formality theorem for complex algebraic varieties." @default.
- W2000737868 created "2016-06-24" @default.
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- W2000737868 date "2007-09-01" @default.
- W2000737868 modified "2023-09-27" @default.
- W2000737868 title "<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML altimg=si1.gif display=inline overflow=scroll><mml:mi>F</mml:mi></mml:math>-isocrystals and homotopy types" @default.
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- W2000737868 doi "https://doi.org/10.1016/j.jpaa.2006.10.006" @default.
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