Rationality problem for norm one tori in small dimensions

Sumito Hasegawa; Akinari Hoshi; Aiichi Yamasaki

doi:10.1090/mcom/3469

Rationality problem for norm one tori in small dimensions

Mathematics of Computation ◽

10.1090/mcom/3469 ◽

2019 ◽

Vol 89 (322) ◽

pp. 923-940 ◽

Cited By ~ 1

Author(s):

Sumito Hasegawa ◽

Akinari Hoshi ◽

Aiichi Yamasaki

Keyword(s):

Rationality Problem

Download Full-text

Rationality Problem for Classifying Spaces of Spinor Groups

Proceedings of the Steklov Institute of Mathematics ◽

10.1134/s0081543819060063 ◽

2019 ◽

Vol 307 (1) ◽

pp. 115-124

Author(s):

Alexander S. Merkurjev

Keyword(s):

Classifying Spaces ◽

Rationality Problem

Download Full-text

The rationality problem for semisimple group varieties

Journal für die reine und angewandte Mathematik (Crelles Journal) ◽

10.1515/crll.1998.108 ◽

1998 ◽

Vol 1998 (504) ◽

pp. 1-28 ◽

Cited By ~ 1

Author(s):

Vladimir P. Platonov ◽

Vladimir I. Chernousov

Keyword(s):

Semisimple Group ◽

Rationality Problem

Download Full-text

The rationality problem for norm one tori

Nagoya Mathematical Journal ◽

10.1017/s0027763000010266 ◽

2011 ◽

Vol 202 ◽

pp. 83-106

Author(s):

Shizuo Endo

Keyword(s):

Galois Group ◽

Galois Extension ◽

Field Extension ◽

Galois Closure ◽

Rationality Problem

AbstractWe consider the problem of whether the norm one torus defined by a finite separable field extensionK/kis stably (or retract) rational overk. This has already been solved for the case whereK/kis a Galois extension. In this paper, we solve the problem for the case whereK/kis a non-Galois extension such that the Galois group of the Galois closure ofK/kis nilpotent or metacyclic.

Download Full-text

Kurt Baier on Reason and Morality

Dialogue ◽

10.1017/s0012217300017686 ◽

1997 ◽

Vol 36 (4) ◽

pp. 813-818

Author(s):

Ishtiyaque Haji

Keyword(s):

Moral Order ◽

Necessary Condition ◽

Moral Conduct ◽

Rationality Problem ◽

Do So

The Rational and the Moral Order, a work of sweeping scope and depth, opens with three problems: the Rationality Problem, briefly, is that the following set is inconsistent, although each of its elements seems true: our conduct cannot be rationally justified unless it promotes our own good; moral conduct is rationally justified; but morality often requires that we do things that do not promote our own good. The Motivation Problem distills to this: can something be a reason for someone to do something without its actually motivating him to do so (the so-called “externalist” position), or is being a motivator a necessary condition of being a reason for that person (the “internalist position”)? Finally, the Sanction Problem notes that, although it seems plausible and generally accepted that immorality should be sanctioned, it seems neither plausible, nor is it generally accepted, that irrationality should be. Why this asymmetry? I restrict my attention, in what follows, to aspects of Baier's fascinating discussion on the Rationality Problem and the Motivation Problem.

Download Full-text