On the failure of the integral Hodge/Tate conjecture for products with projective hypersurfaces
Kees Kok
2023-05-15 15:00-16:00
Online
Speaker: Kees Kok (University of Amsterdam)Time: 15:00-16:00 May 15, 2023 (Monday)
Place: Online (Zoom ID: 336 857 3520 Password: 623286)
Title: On the failure of the integral Hodge/Tate conjecture for products with projective hypersurfaces
Abstract: The failure of the integral Hodge conjecture was first established by Atiyah and Hirzebruch in the 60's. Throughout the years, many techniques have been developed to find even more counter examples. More recently (2012) Colliot-Thélène and Voisin gave an interpretation of the integral Hodge conjecture in degree 2 in terms of unramified cohomology and in 2018, Colliot-Thélène used this, together with a specialization technique to generalize a counter example found by Benoist and Ottem. In this talk, I will explain this specialization technique and show that it can be generalized to recover a counter example found by Shen in 2019. Moreover, by the nature of the argument, there is no need to work over the complex numbers and in turn we obtain a new counter example to the integral Tate conjecture.
