Cyclic algebras over \(p\)-adic curves.

DOI10.1016/j.jalgebra.2007.03.003zbMath1129.16014arXivmath/0604409OpenAlexW2043185072WikidataQ56018681 ScholiaQ56018681MaRDI QIDQ2456203

David J. Saltman

Publication date: 17 October 2007

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0604409

zbMATH Keywords

Brauer groupsnodal pointscentral division algebrasramificationcyclic algebrasalgebraic function fieldsfield extensionscurves over local fields\(p\)-adic curvescurve pointscurves over rings of integers of \(p\)-adic fields

Mathematics Subject Classification ID

Arithmetic ground fields for curves (14H25) Global theory and resolution of singularities (algebro-geometric aspects) (14E15) Curves over finite and local fields (11G20) Local ground fields in algebraic geometry (14G20) Finite-dimensional division rings (16K20) Brauer groups of schemes (14F22) Special surfaces (14J25) Skew fields, division rings (12E15) Algebraic functions and function fields in algebraic geometry (14H05) Algebras and orders, and their zeta functions (11S45)

Related Items

Cyclic length in the Brauer group of a p-adic elliptic curve, Hasse principle for hermitian spaces over semi-global fields, Strong linkage for function fields of surfaces, Square-reflexive polynomials, The \(u\)-invariant of the function fields of \(p\)-adic curves, Reduced Whitehead groups of prime exponent algebras over \(p\)-adic curves, Period-index bounds for arithmetic threefolds, Symbol length in Brauer groups of elliptic curves, Third Galois cohomology group of function fields of curves over number fields, Local-global principle for projective homogeneous spaces of unitary groups, Indecomposability and cyclicity in the p-primary part of the Brauer group of a p-adic curve, Indecomposable and noncrossed product division algebras over function fields of smooth \(p\)-adic curves., Colliot-Thélène's conjecture and finiteness of u-invariants, Tame division algebras of prime period over function fields of \(p\)-adic curves., On Saltman’s p-Adic Curves Papers, The period-index problem for fields of transcendence degree 2, Division algebras over surfaces., Open problems on central simple algebras., A note on the existence of cyclic algebras in division algebras, Applications of patching to quadratic forms and central simple algebras, Formal constructions in the Brauer group of the function field of a 𝑝-adic curve

Cites Work

• Division algebras over Henselian fields.
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