Moving lemmas in mixed characteristic and applications
K-Theory and Homology
2022-02-03 v1
Abstract
The present paper contains new geometric theorems in mixed characteristic case. We derive a bunch of cohomological consequences using these geometric theorems. Among them an isotropy result for quadratic spaces, a purity result for quadratic spaces, a result on the Grothendieck--Serre conjecture for the special linear group of an Azumaya algebra. The Gersten conjecture for the functor K2 is proved. Bloch-Ogus type result is obtained as well. Suslin's exact sequence is derived and its application to a finiteness result is given. A version of the Roitman theorem is proved.
Cite
@article{arxiv.2202.00896,
title = {Moving lemmas in mixed characteristic and applications},
author = {Ivan Panin},
journal= {arXiv preprint arXiv:2202.00896},
year = {2022}
}
Comments
Geometric theorems are stated. Their proofs will be given later