scholarly journals Sextic variety as Galois closure variety of smooth cubic

2013 ◽  
Author(s):  
Hisao Yoshihara
Keyword(s):  
Galois Closure

ON STARK’S CLASS NUMBER CONJECTURE AND THE GENERALISED BRAUER–SIEGEL CONJECTURE

2022 ◽  
pp. 1-13
Author(s):  
PENG-JIE WONG
Keyword(s):  
Class Number ◽  
Number Fields ◽  
Galois Closure ◽  
Stark's Conjecture

Abstract Stark conjectured that for any $h\in \Bbb {N}$ , there are only finitely many CM-fields with class number h. Let $\mathcal {C}$ be the class of number fields L for which L has an almost normal subfield K such that $L/K$ has solvable Galois closure. We prove Stark’s conjecture for $L\in \mathcal {C}$ of degree greater than or equal to 6. Moreover, we show that the generalised Brauer–Siegel conjecture is true for asymptotically good towers of number fields $L\in \mathcal {C}$ and asymptotically bad families of $L\in \mathcal {C}$ .

scholarly journals Nori fundamental gerbe of essentially finite covers and Galois closure of towers of torsors

2019 ◽  
Vol 25 (2) ◽  
Author(s):  
Marco Antei ◽  
Indranil Biswas ◽  
Michel Emsalem ◽  
Fabio Tonini ◽  
Lei Zhang
Keyword(s):  
Galois Closure ◽  
Finite Covers

scholarly journals The rationality problem for norm one tori

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.

scholarly journals Epireflection operators vs perfect morphisms and closed classes of epimorphisms

1972 ◽  
Vol 7 (3) ◽  
pp. 359-366 ◽  
Author(s):  
G.E. Strecker
Keyword(s):  
Galois Closure ◽  
Closure Operations

Operators are defined that yield basic Galois closure operations for almost every category. These give rise to a new and more general approach for characterization of epireflective subcategories, and construction of epireflective hulls. As a by-product, satisfactory characterizations of classes of perfect morphisms and ω-extendable epimorphisms are obtained. Detailed proofs and examples will appear elsewhere.

scholarly journals GALOIS CLOSURE DATA FOR EXTENSIONS OF RINGS

2017 ◽  
Vol 23 (1) ◽  
pp. 41-69 ◽  
Author(s):  
OWEN BIESEL
Keyword(s):  
Galois Closure

The Normal Closure of a Quadratic Extension of a Cyclic Quartic Field

1991 ◽  
Vol 43 (5) ◽  
pp. 1086-1097 ◽  
Author(s):  
Theresa P. Vaughan
Keyword(s):  
Galois Group ◽  
Quadratic Extension ◽  
Normal Closure ◽  
Galois Closure ◽  
Quartic Field

AbstractPierre Barrucand asks the following question (Unsolved Problems, # ASI 88:04, Banff, May 1988, Richard K. Guy, Ed.; also [2, p. 594]). Let K be a cyclic quartic field, and let ξ be a non-square element of K. Let M be the Galois closure of , and let G be the Galois group Gal(M/Q). Find (1) all possible G, (2) conditions on ξ to have such a G, and (3) a list of all possible subfields of M.

scholarly journals The Galois closure of the Garcia–Stichtenoth tower

2007 ◽  
Vol 13 (4) ◽  
pp. 751-761 ◽  
Author(s):  
Alexey Zaytsev
Keyword(s):  
Galois Closure

scholarly journals Families of Galois closure curves for plane quintic curves

2011 ◽  
Vol 342 (1) ◽  
pp. 175-196 ◽  
Author(s):  
Taketo Shirane
Keyword(s):  
Galois Closure ◽  
Quintic Curves ◽  
Plane Quintic
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