On the field of meromorphic functions on a Stein surface
Algebraic Geometry
2025-09-22 v2 Complex Variables
Abstract
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.
Keywords
Cite
@article{arxiv.2410.16809,
title = {On the field of meromorphic functions on a Stein surface},
author = {Olivier Benoist},
journal= {arXiv preprint arXiv:2410.16809},
year = {2025}
}
Comments
43 pages, final version