The Hyodo-Kato theorem for rational homotopy types

Kim, Minhyong; Hain, Richard

doi:10.4310/mrl.2005.v12.n2.a2

Cited by 1 publication

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“…This includes work of Chiarellotto and Le Stum [5], Kim and Hain [19,20], Shiho [35,36], and Vologodsky [42] among others. Thus the main new contribution of this paper is to extend some of the above work to a theory with non-unipotent coefficients, though we also obtain some new results about rational homotopy theory.…”

Section: Acknowledgementsmentioning

confidence: 97%

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F-isocrystals and homotopy types

Olsson

2007

Journal of Pure and Applied Algebra

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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 X C 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-adicétale local systems and Fisocrystals, 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.

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Section: Acknowledgementsmentioning

confidence: 97%

“…In the case when C is generated by the unit isocrystal so that C consists of all unipotent isocrystals, the pointed stack X C is characterized by the crystalline cohomology differential graded algebra of X (the "crystalline rational homotopy type" in the sense of [19,20]). …”

Section: 1)mentioning

confidence: 99%

F-isocrystals and homotopy types

Olsson

2007

Journal of Pure and Applied Algebra

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The Hyodo-Kato theorem for rational homotopy types

Cited by 1 publication

References 7 publications

F-isocrystals and homotopy types

F-isocrystals and homotopy types

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