On Galois cohomology of semisimple groups over local and global fields of positive characteristic, II

2011 ◽  
Vol 270 (3-4) ◽  
pp. 1057-1065 ◽  
Author(s):  
Nguyêñ Quôć Thǎńg
Keyword(s):  
Positive Characteristic ◽  
Galois Cohomology ◽  
Semisimple Groups ◽  
Global Fields

scholarly journals Vanishing of Massey Products and Brauer Groups

2015 ◽  
Vol 58 (4) ◽  
pp. 730-740 ◽  
Author(s):  
Ido Efrat ◽  
Eliyahu Matzri
Keyword(s):  
Prime Number ◽  
Galois Cohomology ◽  
Brauer Groups ◽  
Central Simple Algebras ◽  
Massey Products ◽  
Global Fields ◽  
Root Of Unity ◽  
Simple Algebras ◽  
Central Simple

AbstractLet p be a prime number and F a field containing a root of unity of order p. We relate recent results on vanishing of triple Massey products in the mod-p Galois cohomology of F, due to Hopkins, Wickelgren, Mináč, and Tân, to classical results in the theory of central simple algebras. We prove a stronger form of the vanishing property for global fields.

scholarly journals Local-global principles for Weil–Châtelet divisibility in positive characteristic

2017 ◽  
Vol 163 (2) ◽  
pp. 357-367 ◽  
Author(s):  
BRENDAN CREUTZ ◽  
JOSÉ FELIPE VOLOCH
Keyword(s):  
Elliptic Curve ◽  
Rational Point ◽  
Positive Characteristic ◽  
Number Fields ◽  
Global Field ◽  
Global Fields ◽  
Characteristic 2 ◽  
Global Principles ◽  
Global Principle

AbstractWe extend existing results characterizing Weil-Châtelet divisibility of locally trivial torsors over number fields to global fields of positive characteristic. Building on work of González-Avilés and Tan, we characterize when local-global divisibility holds in such contexts, providing examples showing that these results are optimal. We give an example of an elliptic curve over a global field of characteristic 2 containing a rational point which is locally divisible by 8, but is not divisible by 8 as well as examples showing that the analogous local-global principle for divisibility in the Weil-Châtelet group can also fail.

scholarly journals Descent obstructions and Brauer–Manin obstruction in positive characteristic

2012 ◽  
Vol 12 (3) ◽  
pp. 545-551
Author(s):  
David Harari ◽  
José Felipe Voloch
Keyword(s):  
Positive Characteristic ◽  
Integral Points ◽  
Connected Group ◽  
Group Schemes ◽  
Global Fields

AbstractWe prove that the Brauer–Manin obstruction is the only obstruction to the existence of integral points on affine varieties over global fields of positive characteristic $p$. More precisely, we show that the only obstructions come from étale covers of exponent $p$ or, alternatively, from flat covers coming from torsors under connected group schemes of exponent $p$.

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