Tim Santens

Rational points of bounded height on toric stacks

Recently the Manin conjecture on the number of points of bounded height on varieties was generalized to stacks by Darda-Yasuda. I'll discuss this conjecture, focusing on the special case of $BG$ in which case it reduces to counting $G$-extensions of number fields with respect to certain invariants such as the discriminant. This case has been extensively studied before this conjecture, but viewing this as a problem about counting rational points on stacks can be used to give geometric explanations of some of the phenomena which were observed before.

I'll then talk about some work in progress where I prove this conjecture for toric stacks. Special cases are toric varieties and the stack $BG$ for $G$ finite abelian.