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 journalArticlepeer-review

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.

Translated title of the contributionThird unramified cohomology group of a cubic threefold over a function field in one variable
Original languageFrench
Article number24
JournalEpijournal de Geometrie Algebrique
Volume2
StatePublished - 2018

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

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