Orateur
Description
In various geometric situations, one can describe the category of sheaves on $X \times Y$ (a product of varieties over a field $k$) in terms of sheaves on $X$ and sheaves on $Y$. Results of this form are referred to as categorial Künneth formulas. Eying applications in the function field Langlands program, we have established, in joint work with Hemo and Richarz (https://arxiv.org/abs/2012.02853) such a categorical Künneth formula for étale Weil sheaves. More recently (https://arxiv.org/abs/2503.14416), Richarz and I have proposed a conjecture concerning a categorical Künneth formula for motivic sheaves. In this talk I will present this circle of ideas, give evidence for the conjecture and report on recent results using the interplay between motives and non-commutative motives in order to further extend our knowledge regarding this conjecture.
