The de Rham-Witt complex and p-adic vanishing cycles
Number Theory
2019-08-12 v3 K-Theory and Homology
Abstract
We determine the structure modulo p of the de Rham-Witt complex of a smooth scheme X over a discrete valuation ring of mixed characteristic with log-poles along the special fiber Y and show that the sub-sheaf fixed by the Frobenius is isomorphic to the sheaf of p-adic vanishing cycles. We use this together with results of the second author and Madsen to evaluate the -theory with finite coefficients of the quotient field K of the henselian local ring of X at a generic point of Y. The result affirms the Lichtenbaum-Quillen conjecture for the field K.
Cite
@article{arxiv.math/0312497,
title = {The de Rham-Witt complex and p-adic vanishing cycles},
author = {Thomas Geisser and Lars Hesselholt},
journal= {arXiv preprint arXiv:math/0312497},
year = {2019}
}