A trace formula for varieties over a discretely valued field
| dc.creator | Nicaise, Johannes | |
| dc.date | 2008-05-09 | |
| dc.date | 2008-09-26 | |
| dc.date.accessioned | 2026-07-07T10:05:08Z | |
| dc.date.available | 2026-07-07T10:05:08Z | |
| dc.description | We study the motivic Serre invariant of a smoothly bounded algebraic or rigid variety $X$ over a complete discretely valued field $K$ with perfect residue field $k$. If $K$ has characteristic zero, we extend the definition to arbitrary $K$-varieties using Bittner's presentation of the Grothendieck ring and a process of Néron smoothening of pairs of varieties. The motivic Serre invariant can be considered as a measure for the set of unramified points on $X$. Under certain tameness conditions, it admits a cohomological interpretation by means of a trace formula. In the curve case, we use T. Saito's geometric criterion for cohomological tameness to obtain more detailed results. We discuss some applications to Weil-Châtelet groups, Chow motives, and the structure of the Grothendieck ring. | |
| dc.description | Presentation reorganized; minor errors corrected | |
| dc.identifier | https://arxiv.org/abs/0805.1323 | |
| dc.identifier | http://arxiv.org/abs/0805.1323 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/169922 | |
| dc.subject | Algebraic Geometry | |
| dc.title | A trace formula for varieties over a discretely valued field | |
| dc.type | text |