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

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

2002-05-29

arxiv.org/abs/math/0205306v2

Mathematics

Algebraic Geometry

68 pages, 10pt LaTeX, xy-pic (v2: to appear in Selecta Mathematica)

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Non-commutative geometry, dynamics, and infinity-adic Arakelov geometry does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Non-commutative geometry, dynamics, and infinity-adic Arakelov geometry, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Non-commutative geometry, dynamics, and infinity-adic Arakelov geometry will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-169365