New perspectives in Arakelov geometry

Abstract

In this survey, written for the proceedings of the VII meeting of the CNTA held in May 2002 in Montreal, we describe how Connes' theory of spectral triples provides a unified view, via noncommutative geometry, of the archimedean and the totally split degenerate fibers of an arithmetic surface.

20 pages, 10pt LaTeX, 2 eps figures (v3: some changes for the final version)