English

On the analogy between L-functions and Atiyah-Bott-Lefschetz trace formulas for foliated spaces

Number Theory 2013-07-16 v1

Abstract

This paper is motivated by Deninger's programme. First we prove, using Alvarez Lopez-Kordyukov results, an Atiyah-Bott-Lefschetz trace formula for the cohomology groups associated to a ramified leafwise flat line bundle on a riemannian foliation. Then we argue, by precise computations, that cohomology groups associated to ramified leafwise flat vector bundles on a suitable foliated space (whose existence is still unknown) might be useful to study arithmetic L-functions via Atiyah-Bott-Lefschetz trace formulas.

Keywords

Cite

@article{arxiv.1307.3851,
  title  = {On the analogy between L-functions and Atiyah-Bott-Lefschetz trace formulas for foliated spaces},
  author = {Eric Leichtnam},
  journal= {arXiv preprint arXiv:1307.3851},
  year   = {2013}
}