scholarly journals On the unramified cohomology of certain quotient varieties

2019 ◽  
Vol 296 (1-2) ◽  
pp. 261-273
Author(s):  
Humberto Diaz
Keyword(s):  
Unramified Cohomology ◽  
Quotient Varieties

scholarly journals Degree three unramified cohomology groups

2016 ◽  
Vol 458 ◽  
pp. 120-133 ◽  
Author(s):  
Akinari Hoshi ◽  
Ming-chang Kang ◽  
Aiichi Yamasaki
Keyword(s):  
Cohomology Groups ◽  
Unramified Cohomology

RATIONALITY OF SOME QUOTIENT VARIETIES

1986 ◽  
Vol 54 (2) ◽  
pp. 571-576 ◽  
Author(s):  
F A Bogomolov ◽  
P I Katsylo
Keyword(s):  
Quotient Varieties

scholarly journals Towards a classification of rigid product quotient varieties of Kodaira dimension 0

2021 ◽  
Author(s):  
Ingrid Bauer ◽  
Christian Gleissner
Keyword(s):  
Finite Group ◽  
Finite Groups ◽  
Structure Theorem ◽  
Complete Classification ◽  
Kodaira Dimension ◽  
The Other ◽  
Diagonal Action ◽  
Quotient Varieties ◽  
A Finite Group

AbstractIn this paper the authors study quotients of the product of elliptic curves by a rigid diagonal action of a finite group G. It is shown that only for $$G = {{\,\mathrm{He}\,}}(3), {\mathbb {Z}}_3^2$$ G = He ( 3 ) , Z 3 2 , and only for dimension $$\ge 4$$ ≥ 4 such an action can be free. A complete classification of the singular quotients in dimension 3 and the smooth quotients in dimension 4 is given. For the other finite groups a strong structure theorem for rigid quotients is proven.

scholarly journals Troisi\`eme groupe de cohomologie non ramifi\'ee d'un solide cubique sur un corps de fonctions d'une variable

2018 ◽  
Vol Volume 2 ◽  
Author(s):  
Jean-Louis Colliot-Thélène ◽  
Alena Pirutka
Keyword(s):  
Function Field ◽  
Cohomology Group ◽  
Chow Group ◽  
Hodge Conjecture ◽  
Complex Curve ◽  
The Third ◽  
Generic Fibre ◽  
Nous Montrons ◽  
Unramified Cohomology ◽  
Cubic Threefold

En combinant une m\'ethode de C. Voisin avec la descente galoisienne sur le groupe de Chow en codimension $2$, nous montrons que le troisi\`eme groupe de cohomologie non ramifi\'ee d'un solide cubique lisse d\'efini sur le corps des fonctions d'une courbe complexe est nul. Ceci implique que la conjecture de Hodge enti\`ere pour les classes de degr\'e 4 vaut pour les vari\'et\'es projectives et lisses de dimension 4 fibr\'ees en solides cubiques au-dessus d'une courbe, sans restriction sur les fibres singuli\`eres. --------------- We prove that the third unramified cohomology group of a smooth cubic threefold over the function field of a complex curve vanishes. For this, we combine a method of C. Voisin with Galois descent on the codimension $2$ Chow group. As a corollary, we show that the integral Hodge conjecture holds for degree $4$ classes on smooth projective fourfolds equipped with a fibration over a curve, the generic fibre of which is a smooth cubic threefold, with arbitrary singularities on the special fibres. Comment: in French

Graded Witt ring and unramified cohomology

K-Theory ◽  
1992 ◽  
Vol 6 (1) ◽  
pp. 29-44 ◽  
Author(s):  
R. Parimala ◽  
R. Sridharan
Keyword(s):  
Witt Ring ◽  
Unramified Cohomology

scholarly journals Unramified Cohomology of Finite Groups of Lie Type

2009 ◽  
pp. 55-73 ◽  
Author(s):  
Fedor Bogomolov ◽  
Tihomir Petrov ◽  
Yuri Tschinkel
Keyword(s):  
Finite Groups ◽  
Unramified Cohomology ◽  
Groups Of Lie Type

scholarly journals Degree three unramified cohomology groups and Noether's problem for groups of order 243

2020 ◽  
Vol 544 ◽  
pp. 262-301
Author(s):  
Akinari Hoshi ◽  
Ming-chang Kang ◽  
Aiichi Yamasaki
Keyword(s):  
Cohomology Groups ◽  
Unramified Cohomology ◽  
Noether’S Problem

scholarly journals Modular quotient varieties and singularities by the cyclic group of order 2p

2020 ◽  
Vol 48 (12) ◽  
pp. 5490-5500
Author(s):  
Yin Chen ◽  
Rong Du ◽  
Yun Gao
Keyword(s):  
Cyclic Group ◽  
Quotient Varieties

Unramified cohomology and rationality problems

1993 ◽  
Vol 296 (1) ◽  
pp. 247-268 ◽  
Author(s):  
Emmanuel Peyre
Keyword(s):  
Unramified Cohomology ◽  
Rationality Problems
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