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

2013/07/15 by Éric Leichtnam, Eric Leichtnam, Leichtnam, Eric
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Homotopy and Cohomology in Algebraic Topology #math.NT

paper · pdf · doi:10.48550/arxiv.1307.3851

arxiv created 2013/07/15 · arxiv updated 2013/07/16

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.

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