Applications of patching to quadratic forms and central simple algebras
From MaRDI portal
Publication:1034697
DOI10.1007/s00222-009-0195-5zbMath1259.12003arXiv0809.4481OpenAlexW2077359181MaRDI QIDQ1034697
Julia Hartmann, David Harbater, Daniel Krashen
Publication date: 6 November 2009
Published in: Inventiones Mathematicae (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/0809.4481
Finite-dimensional division rings (16K20) Field arithmetic (12E30) Quadratic forms over local rings and fields (11E08)
Related Items
Cyclic length in the Brauer group of a p-adic elliptic curve, Galois cohomology of function fields of curves over non-archimedean local fields, Hasse principle for hermitian spaces over semi-global fields, Symbol length in the Brauer group of a field, The arithmetic of fields. Abstracts from the workshop held June 16--22, 2013., Quadratic forms and linear algebraic groups. Abstracts from the workshop held June 16--22, 2013., Weierstrass preparation and algebraic invariants, Local-global principle for classical groups over function fields of \(p\)-adic curves, Patching over analytic fibers and the local-global principle, Reduced Whitehead groups of prime exponent algebras over \(p\)-adic curves, On Brauer \(p\)-dimensions and index-exponent relations over finitely-generated field extensions., Period-index bounds for arithmetic threefolds, Period-index and \(u\)-invariant questions for function fields over complete discretely valued fields, Une liste de problèmes, Fibers of flat morphisms and Weierstrass preparation theorem, Local-global principle for projective homogeneous spaces of unitary groups, Some aspects of rational points and rational curves, Weak approximation for homogeneous spaces over some two‐dimensional geometric global fields, Indecomposability and cyclicity in the p-primary part of the Brauer group of a p-adic curve, Local–global principle for reduced norms over function fields of -adic curves, Algebraic groups. Abstracts from the workshop held April 18--24, 2021 (hybrid meeting), Local-global principle for quadratic forms over fraction fields of two-dimensional henselian domains, Patching and weak approximation in isometry groups, Galois module structure of the units modulo \(p^m\) of cyclic extensions of degree \(p^n\), Reduced norms of division algebras over complete discrete valuation fields of local-global type, Linear algebraic groups with good reduction, On the Rost divisibility of henselian discrete valuation fields of cohomological dimension 3, Some Aspects of the Algebraic Theory of Quadratic Forms, Patching subfields of division algebras, Adelic double cosets over semi-global fields, Clifford algebras and the universal invariant, Local rings with zero-dimensional formal fibers, The Pythagoras number and the \(u\)-invariant of Laurent series fields in several variables, Open problems on central simple algebras., On the behaviour of Brauer \(p\)-dimensions under finitely-generated field extensions., The period-index problem in WC-groups. IV: A local transition theorem, Lois de réciprocité supérieures et points rationnels, Local-global principles for norm one tori over semi-global fields, Local triviality for \(G\)-torsors, Differential Galois groups over Laurent series fields, Brauer $p$-dimension of complete discretely valued fields, Diagonal forms of higher degree over function fields of p-adic curves, Local-global principles for homogeneous spaces over some two-dimensional geometric global fields, Noncyclic division algebras over fields of Brauer dimension one, Local-global Galois theory of arithmetic function fields, The \(u\)-invariant of one-dimensional function fields over real power series fields, Local-global principles for zero-cycles on homogeneous spaces over arithmetic function fields, Patching over Berkovich curves and quadratic forms, Local-global principles for constant reductive groups over semi-global fields, Formal constructions in the Brauer group of the function field of a 𝑝-adic curve, Embedding Problems of Division Algebras, Dualité et principe local-global pour les tores sur une courbe au-dessus de ℂ((t )), Unnamed Item, On the \(u\)-invariant of function fields of curves over complete discretely valued fields
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- The \(u\)-invariant of the function fields of \(p\)-adic curves
- The Brauer group of a curve over a strictly local discrete valuation ring
- Patching over fields
- Brauer-Severi schemes of finitely generated algebras
- The period-index problem for the Brauer group of an algebraic surface
- Cyclic algebras over \(p\)-adic curves.
- Rational points in Henselian discrete valuation rings
- Algebraic approximation of structures over complete local rings
- Cohomologie Galoisienne. Cours au College de France, 1962-1963. 4e ed
- Néron Models
- Profinite Groups, Arithmetic, and Geometry. (AM-67)
- On the arithmetic of abelian varieties