Zeta functions of regular arithmetic schemes at $s=0$
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | MORIN, Baptiste | |
| dc.date.accessioned | 2024-04-04T02:56:35Z | |
| dc.date.available | 2024-04-04T02:56:35Z | |
| dc.date.issued | 2014 | |
| dc.identifier.issn | 0012-7094 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/192478 | |
| dc.description.abstractEn | In [35] Lichtenbaum conjectured the existence of a Weil-étale cohomology in order to describe the vanishing order and the special value of the Zeta function of an arithmetic scheme X at s = 0 in terms of Euler-Poincaré characteristics. Assuming the (conjectured) finite generation of some étale motivic cohomology groups we construct such a cohomology theory for regular schemes proper over Spec(Z). In particular, we obtain (unconditionally) the right Weil-étale cohomology for geometrically cellular schemes over number rings. We state a conjecture expressing the vanishing order and the special value up to sign of the Zeta function ⇣(X , s) at s = 0 in terms of a perfect complex of abelian groups R W,c(X , Z). Then we relate this conjecture to Soulé's conjecture and to the Tamagawa number conjecture of Bloch-Kato, and deduce its validity in simple cases. | |
| dc.language.iso | en | |
| dc.publisher | Duke University Press | |
| dc.subject.en | Weil-étale cohomology | |
| dc.subject.en | special values of Zeta functions | |
| dc.subject.en | motivic cohomology | |
| dc.subject.en | regulators | |
| dc.title.en | Zeta functions of regular arithmetic schemes at $s=0$ | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.1215/00127094-2681387 | |
| dc.subject.hal | Mathématiques [math]/Théorie des nombres [math.NT] | |
| dc.subject.hal | Mathématiques [math]/Géométrie algébrique [math.AG] | |
| bordeaux.journal | Duke Mathematical Journal | |
| bordeaux.page | 1263-1336 | |
| bordeaux.volume | 163 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.issue | 7 | |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-02484903 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-02484903v1 | |
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