Division algebras over nonlocal Henselian surfaces

Timothy J. Ford

Vol. 147 (1991), No. 2, 301–310

DOI: 10.2140/pjm.1991.147.301

Abstract

Let R be the coordinate ring of an integral affine algebraic surface, R the henselization of R along a reduced, connected curve and K the quotient field of R. Then every central K-division algebra D of exponent n in B(K) is cyclic of degree n. If K is the quotient field of R and D is a central K-division algebra of exponent n with ramification divisor Z on SpecR, then there is an étale neighborhood U → SpecR of Z such that upon restriction to K(U), D is a cyclic algebra of exponent n and index n.

Mathematical Subject Classification 2000

Primary: 12G05

Secondary: 12E15, 13A20, 14F20

Milestones

Received: 8 May 1989

Published: 1 February 1991