Troisième groupe de cohomologie non ramifiée d'un solide cubique sur un corps de fonctions d'une variable

Translated title of the contribution: Third unramified cohomology group of a cubic threefold over a function field in one variable

Jean Louis Colliot-Thélène, Alena Pirutka

Research output: Contribution to journalArticle

Abstract

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.

Original languageFrench
Article number24
JournalEpijournal de Geometrie Algebrique
Volume2
StatePublished - Jan 1 2018

Fingerprint

Cohomology of Groups
Function Fields
Threefolds
Fiber
Chow Groups
Curve Complex
Galois
Fibration
Descent
Codimension
Vanish
Corollary
Singularity
Curve
Arbitrary

Keywords

  • Chow groups
  • Codimension 2 cycles
  • Family of cubic hypersurfaces
  • Integral Hodge conjecture
  • Intermediate jacobian
  • Unramified cohomology

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Geometry and Topology

Cite this

Troisième groupe de cohomologie non ramifiée d'un solide cubique sur un corps de fonctions d'une variable. / Colliot-Thélène, Jean Louis; Pirutka, Alena.

In: Epijournal de Geometrie Algebrique, Vol. 2, 24, 01.01.2018.

Research output: Contribution to journalArticle

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