Archimedean cohomology revisited
| dc.creator | Consani, Caterina | |
| dc.creator | Marcolli, Matilde | |
| dc.date | 2004-07-28 | |
| dc.date.accessioned | 2026-07-07T05:10:46Z | |
| dc.date.available | 2026-07-07T05:10:46Z | |
| dc.description | Archimedean cohomology provides a cohomological interpretation for the calculation of the local L-factors at archimedean places as zeta regularized determinant of a log of Frobenius. In this paper we investigate further the properties of the Lefschetz and log of monodromy operators on this cohomology. We use the Connes-Kreimer formalism of renormalization to obtain a fuchsian connection whose residue is the log of the monodromy. We also present a dictionary of analogies between the geometry of a tubular neighborhood of the ``fiber at arithmetic infinity'' of an arithmetic variety and the complex of nearby cycles in the geometry of a degeneration over a disk, and we recall Deninger's approach to the archimedean cohomology through an interpretation as global sections of a analytic Rees sheaf. We show that action of the Lefschetz, the log of monodromy and the log of Frobenius on the archimedean cohomology combine to determine a spectral triple in the sense of Connes. The archimedean part of the Hasse-Weil L-function appears as a zeta function of this spectral triple. We also outline some formal analogies between this cohomological theory at arithmetic infinity and Givental's homological geometry on loop spaces. | |
| dc.description | 28 pages LaTeX 3 eps figures | |
| dc.identifier | https://arxiv.org/abs/math/0407480 | |
| dc.identifier | http://arxiv.org/abs/math/0407480 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/72035 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Number Theory | |
| dc.subject | Quantum Algebra | |
| dc.subject | 14G40, 58B34 | |
| dc.title | Archimedean cohomology revisited | |
| dc.type | text |