Galois Cohomology of Function Fields of Curves over Non-archimedean Local Fields

2021/05/17 by Saurabh Gosavi, Gosavi, Saurabh
Mathematics · Social Sciences · #Algebraic Geometry and Number Theory #Vietnamese History and Culture Studies #Historical and Political Studies

paper · pdf · doi:10.48550/arxiv.2105.08172

Abstract

Let F be the function field of a curve over a non-archimedean local field. Let m ≥ 2 be an integer coprime to the characteristic of the residue field of the local field. In this article, we show that every element in H³(F, μ_m^{⊗ 2}) is of the form χ∪ (f) ∪ (g), where χ is in H¹(F, ℤ/mℤ) and (f), (g) in H¹(F, μ_m). This extends a result of Parimala and Suresh, where they show this when m is prime and when F contains μ_m.

Related

• Galois Cohomology of Reductive Groups over Function Fields over ℂ((t))
• Local-global principles for Galois cohomology
• Third Galois cohomology group of function fields of curves over number fields
• Recovering function fields from their integral ℓ-adic cohomology with the Galois action
• Curves over higher local fields