Arithmetic characteristic classes of automorphic vector bundles

Details Arithmetic characteristic classes of automorphic vector bundles Arithmetic characteristic classes of automorphic vector bundles

2005-02-04

arxiv.org/abs/math/0502085v1

Mathematics

Algebraic Geometry

104 pages

Scientific paper

We develop a theory of arithmetic characteristic classes of (fully decomposed) automorphic vector bundles equipped with an invariant hermitian metric. These characteristic classes have values in an arithmetic Chow ring constructed by means of differential forms with certain log-log type singularities. We first study the cohomological properties of log-log differential forms, prove a Poincar\'e lemma for them and construct the corresponding arithmetic Chow groups. Then we introduce the notion of log-singular hermitian vector bundles, which is a variant of the good hermitian vector bundles introduced by Mumford, and we develop the theory of arithmetic characteristic classes. Finally we prove that the hermitian metrics of automorphic vector bundles considered by Mumford are not only good but also log-singular. The theory presented here provides the theoretical background which is required in the formulation of the conjectures of Maillot-Roessler in the semi-abelian case and which is needed to extend Kudla's program about arithmetic intersections on Shimura varieties to the non compact case.

Affiliated with

Also associated with

No associations

Rating

Arithmetic characteristic classes of automorphic vector bundles 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 Arithmetic characteristic classes of automorphic vector bundles, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Arithmetic characteristic classes of automorphic vector bundles will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-528106