A BETTER COMPARISON OF cdh- AND ldh-COHOMOLOGIES. (13th December 2019) - KELLY, SHANE
Abstract : In order to work with non-Nagata rings which are Nagata "up-to-completely-decomposed-universal-homeomorphism, " specifically finite rank Hensel valuation rings, we introduce the notions of pseudo-integral closure, pseudo-normalization, and pseudo-Hensel valuation ring . We use this notion to give a shorter and more direct proof that H_cdh^n(X, F_cdh)=H_ldh^n(X, F_ldh) for homotopy sheaves F of modules over the Z_(l) -linear motivic Eilenberg–Maclane spectrum. This comparison is an alternative to the first half of the author's volume Astérisque 391 whose main theorem is a cdh-descent result for Voevodsky motives. The motivating new insight is really accepting that Voevodsky's motivic cohomology (with Z[1p] -coefficients) is invariant not just for nilpotent thickenings, but for all universal homeomorphisms.