Amitsur cohomology for certain extensions of rings of algebraic integers

Kenneth Mandelberg

Vol. 59 (1975), No. 1, 161–197

DOI: 10.2140/pjm.1975.59.161

Abstract

The Amitsur cohomology groups H¹(S∕R,Pic) and H²(S∕R,U) are computed in a number of cases where R ⊆ S are rings of algebraic integers, with most specific results when R is Z and S is the ring of integers in a quadratic nmher field. These results give information about the Brauer group Br (S∕R), which gives a new proof of its vanishing when R = Z and S is in an infinite class of quadratic extensions.

Mathematical Subject Classification 2000

Primary: 12G05

Milestones

Received: 10 August 1973

Revised: 22 October 1974

Published: 1 July 1975