TY - JOUR
T1 - Troisième groupe de cohomologie non ramifiée d'un solide cubique sur un corps de fonctions d'une variable
AU - Colliot-Thélène, Jean Louis
AU - Pirutka, Alena
N1 - Funding Information:
Remerciements. Ce travail a commencé à Vienne pendant le programme “Advances in Birational Geometry 2017" ; nous remercions l’Institut Schrödinger pour son hospitalité et Ludmil Katzarkov pour avoir lancé ce programme. Le deuxième auteur remercie le Laboratoire de Symétrie Miroir NRU HSE, RF Government grant, ag. 14.641.31.0001 et le NSF grant 1601680 pour leurs soutiens financiers. Le premier auteur remercie l’Institut Courant, NYU, pour son hospitalité.
Publisher Copyright:
© by the author(s)
Copyright:
Copyright 2019 Elsevier B.V., All rights reserved.
PY - 2018
Y1 - 2018
N2 - 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.
AB - 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.
KW - Chow groups
KW - Codimension 2 cycles
KW - Family of cubic hypersurfaces
KW - Integral Hodge conjecture
KW - Intermediate jacobian
KW - Unramified cohomology
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M3 - Article
AN - SCOPUS:85069558584
SN - 2491-6765
VL - 2
JO - Epijournal de Geometrie Algebrique
JF - Epijournal de Geometrie Algebrique
M1 - 24
ER -