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arXiv · 1409.7530

On the Witt vector Frobenius

Christopher Davis·Kiran S. Kedlaya
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Abstract

We study the kernel and cokernel of the Frobenius map on the $p$-typical Witt vectors of a commutative ring, not necessarily of characteristic $p$. We give some equivalent conditions to surjectivity of the Frobenus map on both finite and infinite length Witt vectors; the former condition turns out to be stable under certain integral extensions, a fact which relates closely to a generalization of Faltings's almost purity theorem.

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Christopher Davis, Kiran S. Kedlaya. 2014-09-26. On the Witt vector Frobenius. https://doi.org/10.1090/s0002-9939-2014-11953-8

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