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

Abstract

[EN] 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,\Sigma_C).