On cohomology of locally profinite sets

Abstract

We construct a locally profinite set of cardinality ${\aleph }_{\omega }$ with infinitely many first cohomology classes of which any distinct finite product does not vanish. Building on this, we construct the first example of a nondescendable faithfully flat map between commutative rings of cardinality ${\aleph }_{\omega }$ within Zermelo--Fraenkel set theory.

7 pages