2017/11/30 by Vlerë Mehmeti · 7 citations
Computer Science · Mathematics · #Algebraic Geometry and Number Theory #Calculus (dental) #Context (archaeology) #Epistemology #Field (mathematics) #Geometry #Holomorphic and Operator Theory #Invariant (physics) #Isotropy #Mathematical physics #Mathematics #Physics #Polynomial and algebraic computation #Pure mathematics #Quadratic equation #Quadratic function #Simple (philosophy) #math.AG #math.NT #math.RA #msc:11E08 #msc:14G22
paper · pdf · doi:10.1112/s0010437x19007632
published in Compositio Mathematica 155(12), 2399-2438 (Cambridge University Press) · 42 pages. Proved a local-global principle with respect to completions and generalized the one obtained in the previous version. Added a section showing that Harbater, Hartmann and Krashen's local-global principle can be obtained as a consequence of ours and that the converse is true as well under certain conditions. Final version. To appear in Compositio Math
arxiv created 2019/10/28 · openalex publication_date 2019/11/11 · arxiv updated 2019/11/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We extend field patching to the setting of Berkovich analytic geometry and use it to prove a local–global principle over function fields of analytic curves with respect to completions. In the context of quadratic forms, we combine it with sufficient conditions for local isotropy over a Berkovich curve to obtain applications on the u -invariant. The patching method we adapt was introduced by Harbater and Hartmann [ Patching over fields , Israel J. Math. 176 (2010), 61–107] and further developed by these two authors and Krashen [ Applications of patching to quadratic forms and central simple algebras , Invent. Math. 178 (2009), 231–263]. The results presented in this paper generalize those of Harbater, Hartmann, and Krashen [ Applications of patching to quadratic forms and central simple algebras , Invent. Math. 178 (2009), 231–263] on the local–global principle and quadratic forms.