Construction de Variétés de Groupes Exceptionnels Non $k$-Rationnelles

2015 ◽  
Vol 116 (2) ◽  
pp. 182
Author(s):  
Philippe Gille
Keyword(s):  
Weak Approximation ◽  
Exceptional Groups ◽  
Rational Varieties

Our goal is to construct non $k$-rational varieties of exceptional groups. The relevant invariant is the defect of weak approximation.

A Weak Approximation of SDEs with Asymptotic Expansion

2013 ◽  
Author(s):  
Akihiko Takahashi ◽  
Toshihiro Yamada
Keyword(s):  
Asymptotic Expansion ◽  
Weak Approximation

Cancellation of anomalies in supersymmetric sigma models based on exceptional groups

1986 ◽  
Vol 269 (3-4) ◽  
pp. 575-586 ◽  
Author(s):  
T. Yanagida ◽  
Yukinori Yasui
Keyword(s):  
Sigma Models ◽  
Exceptional Groups

scholarly journals Explicit methods for the Hasse norm principle and applications to A n and S n extensions

2021 ◽  
pp. 1-41
Author(s):  
ANDRÉ MACEDO ◽  
RACHEL NEWTON
Keyword(s):  
Galois Group ◽  
Computational Methods ◽  
Number Fields ◽  
Normal Closure ◽  
Explicit Methods ◽  
Weak Approximation ◽  
Norm Principle ◽  
Theoretical Results

Abstract Let K/k be an extension of number fields. We describe theoretical results and computational methods for calculating the obstruction to the Hasse norm principle for K/k and the defect of weak approximation for the norm one torus \[R_{K/k}^1{\mathbb{G}_m}\] . We apply our techniques to give explicit and computable formulae for the obstruction to the Hasse norm principle and the defect of weak approximation when the normal closure of K/k has symmetric or alternating Galois group.

scholarly journals Finite simple exceptional groups of Lie type in which all subgroups of odd index are pronormal

2020 ◽  
Vol 23 (6) ◽  
pp. 999-1016
Author(s):  
Anatoly S. Kondrat’ev ◽  
Natalia V. Maslova ◽  
Danila O. Revin
Keyword(s):  
Simple Groups ◽  
Finite Simple Groups ◽  
Exceptional Groups ◽  
Odd Index ◽  
Groups Of Lie Type

AbstractA subgroup H of a group G is said to be pronormal in G if H and {H^{g}} are conjugate in {\langle H,H^{g}\rangle} for every {g\in G}. In this paper, we determine the finite simple groups of type {E_{6}(q)} and {{}^{2}E_{6}(q)} in which all the subgroups of odd index are pronormal. Thus, we complete a classification of finite simple exceptional groups of Lie type in which all the subgroups of odd index are pronormal.

scholarly journals Failures of weak approximation in families

2016 ◽  
Vol 152 (7) ◽  
pp. 1435-1475 ◽  
Author(s):  
M. J. Bright ◽  
T. D. Browning ◽  
D. Loughran
Keyword(s):  
Number Field ◽  
Weak Approximation

Given a family of varieties$X\rightarrow \mathbb{P}^{n}$over a number field, we determine conditions under which there is a Brauer–Manin obstruction to weak approximation for 100% of the fibres which are everywhere locally soluble.

Sign in / Sign up

Export Citation Format

Share Document