Overconvergent Witt Vectors
Christopher Davis, Andreas Langer, Thomas Zink

TL;DR
This paper introduces overconvergent Witt vectors as a subring of Witt vectors for finitely generated algebras over a field of characteristic p, establishing their sheaf property and laying groundwork for a new cohomology theory.
Contribution
It defines overconvergent Witt vectors and proves they form an étale sheaf on schemes, enabling new approaches in p-adic cohomology theories.
Findings
Overconvergent Witt vectors form an étale sheaf.
The subring is well-behaved on schemes of finite type.
Foundation laid for overconvergent de Rham-Witt complex.
Abstract
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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