On the Witt vector Frobenius
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On the Witt vector Frobenius. / Davis, Christopher James; Kedlaya, Kiran.
I: Proceedings of the American Mathematical Society, Bind 142, Nr. 7, 2014, s. 2211-2226.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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TY - JOUR
T1 - On the Witt vector Frobenius
AU - Davis, Christopher James
AU - Kedlaya, Kiran
PY - 2014
Y1 - 2014
N2 - 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 many equivalent conditions to surjectivity of the Frobenius map on both finite and infinite length Witt vectors. In particular, surjectivity on finite Witt vectors turns out to be stable under certain integral extensions; this provides a clean formulation of a strong generalization of Faltings’s almost purity theorem from p-adic Hodge theory, incorporating recent improvements by Kedlaya–Liu and by Scholze.
AB - 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 many equivalent conditions to surjectivity of the Frobenius map on both finite and infinite length Witt vectors. In particular, surjectivity on finite Witt vectors turns out to be stable under certain integral extensions; this provides a clean formulation of a strong generalization of Faltings’s almost purity theorem from p-adic Hodge theory, incorporating recent improvements by Kedlaya–Liu and by Scholze.
U2 - 10.1090/S0002-9939-2014-11953-8
DO - 10.1090/S0002-9939-2014-11953-8
M3 - Journal article
VL - 142
SP - 2211
EP - 2226
JO - Proceedings of the American Mathematical Society
JF - Proceedings of the American Mathematical Society
SN - 0002-9939
IS - 7
ER -
ID: 64389320