2024/10/22 by Olivier Benoist, Benoist, Olivier
Mathematics · #Holomorphic and Operator Theory #Meromorphic and Entire Functions #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.2410.16809
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.