Overconvergent Witt Vectors

Details Overconvergent Witt Vectors Overconvergent Witt Vectors

2010-08-02

arxiv.org/abs/1008.0305v1

Mathematics

Algebraic Geometry

25 pages

Scientific paper

Let A be a finitely generated algebra over a field K of characteristic p >0. We introduce a subring of the ring of Witt vectors W(A). We call it the ring of overconvergent Witt vectors. We prove that on a scheme X of finite type over K the overconvergent Witt vectors are an \'etale sheaf. In a forthcoming paper (Annales ENS) we define an overconvergent de Rham-Witt complex on a smooth scheme X over a perfect field K whose hypercohomology is the rigid cohomology of X in the sense of Berthelot.

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