On the field of meromorphic functions on a Stein surface
Fuente:
arXiv
Enregistré dans:
| Auteur principal: | |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866909796414783488 |
|---|---|
| author | Benoist, Olivier |
| author_facet | Benoist, Olivier |
| contents | We prove that fields of meromorphic functions on Stein surfaces have cohomological dimension 2, and solve the period-index problem and Serre's conjecture II for these fields. We obtain analogous results for fields of real meromorphic functions on Stein surfaces equipped with an antiholomorphic involution. We deduce an optimal quantitative solution to Hilbert's 17th problem on analytic surfaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_16809 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the field of meromorphic functions on a Stein surface Benoist, Olivier Algebraic Geometry Complex Variables 32E10, 32A20, 12G05, 12J15, 11E25 We prove that fields of meromorphic functions on Stein surfaces have cohomological dimension 2, and solve the period-index problem and Serre's conjecture II for these fields. We obtain analogous results for fields of real meromorphic functions on Stein surfaces equipped with an antiholomorphic involution. We deduce an optimal quantitative solution to Hilbert's 17th problem on analytic surfaces. |
| title | On the field of meromorphic functions on a Stein surface |
| topic | Algebraic Geometry Complex Variables 32E10, 32A20, 12G05, 12J15, 11E25 |
| url | https://arxiv.org/abs/2410.16809 |