Moving lemmas in mixed characteristic and applications

2022/02/02 by Panin, Ivan · 2 citations
#FOS: Mathematics #K-Theory and Homology (math.KT)

paper · doi:10.48550/arxiv.2202.00896

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.

Cited by

• Gersten conjecture for K-theory on Henselian schemes and ϕ-motivic localisation
• The Bloch-Ogus Theorem over DVR

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