A De Rham-Witt approach to crystalline rational homotopy theory

Details A De Rham-Witt approach to crystalline rational homotopy theory A De Rham-Witt approach to crystalline rational homotopy theory

2001-05-01

arxiv.org/abs/math/0105008v4

Mathematics

Algebraic Geometry

Scope of comparison isomorphism narrowed. General case dealt with in a separate preprint. Also, some typos corrected

Scientific paper

We construct the crystalline fundamental group of a semi-stable variety over a field of positive characteristic using the log De Rham-Witt complex and Navarro-Aznar's derived Thom-Whitney functor. This approach gives a relatively direct comparison theorem with the De Rham fundamental group in the liftable case. Also, we get a natural weight filtration which makes the coordinate ring of the crystalline fundamental group into a mixed isocrystal when the variety is defined over a finite field. Finally, the monodromy operator on the crystalline fundamental group is used to prove a crystalline analogue of Oda's good reduction criterion for curves.

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