Non-commutative geometry, dynamics, and infinity-adic Arakelov geometry

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In Arakelov theory a completion of an arithmetic surface is achieved by enlarging the group of divisors by formal linear combinations of the ``closed fibers at infinity''. Manin described the dual graph of any such closed fiber in terms of an infinite tangle of bounded geodesics in a hyperbolic handlebody endowed with a Schottky uniformization. In this paper we consider arithmetic surfaces over the ring of integers in a number field, with fibers of genus $g\geq 2$. We use Connes' theory of spectral triples to relate the hyperbolic geometry of the handlebody to Deninger's Archimedean cohomology and the cohomology of the cone of the local monodromy $N$ at arithmetic infinity as introduced by the first author of this paper.
68 pages, 10pt LaTeX, xy-pic (v2: to appear in Selecta Mathematica)

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Algebraic Geometry, Differential Geometry, Number Theory, 58B34, 14G40, 37F30

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http://salesiana.dossiersoluciones.com/handle/123456789/64179

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0205306
 http://arxiv.org/abs/math/0205306

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arXiv