Central extensions, symbols and reciprocity laws on GL(n,ℱ)

Fernando Pablos Romo

Vol. 234 (2008), No. 1, 137–159

DOI: 10.2140/pjm.2008.234.137

Abstract

For a discrete valuation field ℱ, using commensurability on valuation rings, we construct arithmetic symbols on the linear group GL(n,ℱ) that generalize classical symbols such as the tame symbol and the Hilbert norm residue symbol on an algebraic curve. We also offer reciprocity laws for these symbols on GL(n,Σ_C).

Keywords

arithmetic symbols, reciprocity laws, discrete valuation field, linear group, algebraic curve

Mathematical Subject Classification 2000

Primary: 19F15

Secondary: 11R58, 14H05

Milestones

Received: 10 April 2007

Revised: 3 October 2007

Accepted: 8 October 2007

Published: 1 January 2008