Refinements to Patching and Applications to Field Invariants

DOI10.1093/imrn/rnu278zbMath1386.14101arXiv1404.4349OpenAlexW2130746220MaRDI QIDQ3451038

David Harbater, Daniel Krashen, Julia Hartmann

Publication date: 10 November 2015

Published in: International Mathematics Research Notices (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1404.4349

zbMATH Keywords

\(u\)-invariantWitt ringquadratic formpatchingBrauer grouplocal-global principleperiod-index problemfunction field of a curvetwo-dimensional complete domain

Mathematics Subject Classification ID

Quadratic forms over general fields (11E04) Arithmetic ground fields for curves (14H25) Algebraic theory of quadratic forms; Witt groups and rings (11E81) Finite-dimensional division rings (16K20) Brauer groups of schemes (14F22) Formal power series rings (13F25) Brauer groups (algebraic aspects) (16K50) Algebraic functions and function fields in algebraic geometry (14H05) Valued fields (12J10)

Related Items (10)

Hasse principle for hermitian spaces over semi-global fields ⋮ Local-global principle for classical groups over function fields of \(p\)-adic curves ⋮ Local-global principle for projective homogeneous spaces of unitary groups ⋮ Local–global principle for reduced norms over function fields of -adic curves ⋮ Bounding the Pythagoras number of a field by \(2^n +1\) ⋮ Reduced norms of division algebras over complete discrete valuation fields of local-global type ⋮ Differential embedding problems over Laurent series fields ⋮ Local-global Galois theory of arithmetic function fields ⋮ Local-global principles for zero-cycles on homogeneous spaces over arithmetic function fields ⋮ Local-global principles for constant reductive groups over semi-global fields

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