Non-commutative geometry, dynamics, and infinity-adic Arakelov geometry
| dc.creator | Consani, Caterina | |
| dc.creator | Marcolli, Matilde | |
| dc.date | 2002-05-29 | |
| dc.date | 2003-10-27 | |
| dc.date.accessioned | 2026-07-07T04:48:46Z | |
| dc.date.available | 2026-07-07T04:48:46Z | |
| dc.description | 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. | |
| dc.description | 68 pages, 10pt LaTeX, xy-pic (v2: to appear in Selecta Mathematica) | |
| dc.identifier | https://arxiv.org/abs/math/0205306 | |
| dc.identifier | http://arxiv.org/abs/math/0205306 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/64179 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Differential Geometry | |
| dc.subject | Number Theory | |
| dc.subject | 58B34, 14G40, 37F30 | |
| dc.title | Non-commutative geometry, dynamics, and infinity-adic Arakelov geometry | |
| dc.type | text |