Unramified cohomology and rationality problems

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

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

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 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

Automorphism groups and invariant theory on ℙN

2018 ◽  
Vol 17 (09) ◽  
pp. 1850162 ◽  
Author(s):  
João Alberto de Faria ◽  
Benjamin Hutz
Keyword(s):  
Fixed Point ◽  
Automorphism Group ◽  
Invariant Theory ◽  
Automorphism Groups ◽  
Finite Subgroup ◽  
Fixed Point Algorithm ◽  
Projective Linear Group ◽  
Rationality Problems ◽  
Stabilizer Group ◽  
A Finite Group

Let [Formula: see text] be a field and [Formula: see text] a morphism. There is a natural conjugation action on the space of such morphisms by elements of the projective linear group [Formula: see text]. The group of automorphisms, or stabilizer group, of a given [Formula: see text] for this action is known to be a finite group. In this paper, we apply methods of invariant theory to automorphism groups by addressing two mainly computational problems. First, given a finite subgroup of [Formula: see text], determine endomorphisms of [Formula: see text] with that group as a subgroup of its automorphism group. In particular, we show that every finite subgroup occurs infinitely often and discuss some associated rationality problems. Inversely, given an endomorphism, determine its automorphism group. In particular, we extend the Faber–Manes–Viray fixed-point algorithm for [Formula: see text] to endomorphisms of [Formula: see text]. A key component is an explicit bound on the size of the automorphism group depending on the degree of the endomorphism.

scholarly journals ℤ[1/p]-motivic resolution of singularities

2011 ◽  
Vol 147 (5) ◽  
pp. 1434-1446 ◽  
Author(s):  
M. V. Bondarko
Keyword(s):  
Preceding Paper ◽  
Resolution Of Singularities ◽  
Cohomology Theory ◽  
Spectral Sequences ◽  
Perfect Field ◽  
Chow Motives ◽  
Unramified Cohomology ◽  
Weight Structure ◽  
Weight Structures

AbstractThe main goal of this paper is to deduce (from a recent resolution of singularities result of Gabber) the following fact: (effective) Chow motives with ℤ[1/p]-coefficients over a perfect field k of characteristic p generate the category DMeffgm[1/p] (of effective geometric Voevodsky’s motives with ℤ[1/p]-coefficients). It follows that DMeffgm[1/p] can be endowed with a Chow weight structure wChow whose heart is Choweff[1/p] (weight structures were introduced in a preceding paper, where the existence of wChow for DMeffgmℚ was also proved). As shown in previous papers, this statement immediately yields the existence of a conservative weight complex functor DMeffgm[1/p]→Kb (Choweff [1/p]) (which induces an isomorphism on K0-groups), as well as the existence of canonical and functorial (Chow)-weight spectral sequences and weight filtrations for any cohomology theory on DMeffgm[1/p] . We also mention a certain Chow t-structure for DMeff−[1/p] and relate it with unramified cohomology.

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