Submission date: 28 October 2015

Abstract:

Through a cascade of generalizations of results and definitions, we establish a theory of integration which works uniformly in all p-adic fields, regardless of ramification degrees, that is, for all finite field extensions of Q_p for all p. The framework is stable under integration and under Fourier transformation and implies various kinds of uniformity for integrals and for exceptional loci. Note that this bears nothing new in the positive characteristic case (which remains mysterious), and neither in the case of large residue field characteristic (which is already well understood).

Mathematics Subject Classification: 14E18 (Primary), 03C10, 11S80, 11Q25, 40J99 (Secondary)

Keywords and phrases:

Full text arXiv 1510.08250: pdf, ps.