Local-global principles for hermitian spaces over semi-global fields

2022/03/17 by Guhan, Jayanth
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #FOS: Mathematics #Geometry and complex manifolds #Number Theory (math.NT) #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.2203.09651

openalex publication_date 2022/03/17 · openalex created_date 2022/04/03 · openalex updated_date 2026/07/28

Abstract

Let K be a complete discrete valued field with residue field k and F the function field of a curve over K. Let A ∈ ₂Br(F) be a central simple algebra with an involution σ of any kind and F₀ =F^σ. Let h be an hermitian space over (A, σ) and G = SU(A, σ, h) if σ is of first kind and G = U(A, σ, h) if σ is of second kind. Suppose that char(k) ≠ 2 and ind(A)≤ 4. Then we prove that projective homogeneous spaces under G over F₀ satisfy a local-global principle for rational points with respect to discrete valuations of F.

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