# Matthias Paulsen (Hannover) - Unirational counterexamples to the IHC of torsion type

Counterexamples to the integral Hodge conjecture can arise either from
torsion cohomology classes (as in Atiyah's and Hirzebruch's original
counterexample from 1961) or from non-torsion classes (as first seen in
Kollár's counterexample from 1991). After Voisin proved the IHC for
uniruled threefolds, Schreieder found a unirational fourfold where the
IHC fails. His construction of a non-algebraic Hodge class relies on
abstract arguments with unramified cohomology. It was an open question
whether this class is of torsion type. In this talk, I want to explain a
new method that gives an explicit geometric description of the
unramified cohomology class appearing in his argument. In particular,
this approach allows to prove that Schreieder's unirational
counterexample is of torsion type.

Published Sep. 13, 2022 12:37 PM
- Last modified Nov. 16, 2022 8:59 PM