F–isocrystals and Homotopy Types (f–isocristaux Et Types D’homotopie)
نویسندگان
چکیده
We study a positive characteristic analog 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 analog 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.
منابع مشابه
Braiding of differential forms and homotopy types
Let k be an arbitrary commutative ring. We associate fonctorially to any simplicial set X a differential graded algebra Ŵ∗(X) with a globally defined braiding, which is an improvement of a previous work [3,4]. If k= Z and with some mild finiteness conditions on X, we show that the quasi-isomorphisms class of Ŵ∗(X) as a braided differential graded algebra determines the p-adic homotopy type of X...
متن کاملOn Bruhat posets associated to compositions ∗
The purpose of this work is to initiate a combinatorial study of the Bruhat-Chevalley ordering on certain sets of permutations obtained by omitting the parentheses from their standard cyclic notation. In particular, we show that these sets form bounded, graded, unimodal, rank-symmetric and EL-shellable posets. Moreover, we determine the homotopy types of the associated order complexes. Résumé. ...
متن کاملOptimal Control of the Atmospheric Reentry of a Space Shuttle by an Homotopy Method
This paper deals with the optimal control problem of the atmospheric reentry of a space shuttle with a second-order state constraint on the thermal flux. We solve the problem using the shooting algorithm combined with an homotopy method which automatically determines the structure of the optimal trajectory (composed of one boundary arc and one touch point). Key-words: Optimal control, State con...
متن کاملMorphisms of F-isocrystals and the Finite Monodromy Theorem for Unit-root F-isocrystals
We discuss Tate-type problems for F-isocrystals, that is, the full faithfulness of the natural restriction functors between categories of overconvergent F-isocrystals on schemes of positive characteristic. We prove it in the cases of unit-root F-isocrystals. Using this result, we prove that an overconvergent unit-root F-isocrystal has a finite monodromy.
متن کاملOverholonomicity of overconvergent F-isocrystals over smooth varieties
We prove the overholonomicity of overconvergent F-isocrystals over smooth varieties. This implies that the notions of overholonomicity and devissability in overconvergent F-isocrystals are equivalent. Then the overholonomicity is stable under tensor products. So, the overholonomicity gives a p-adic cohomology stable under Grothendieck’s cohomological operations.
متن کامل