Manin-Peyre conjecture for weighted projective stacks

Abstract: Manin-Peyre conjecture predicts the number of rational points of bounded height on algebraic varieties. The constants appearing in the prediction are expressed using arithmetic and geometric invariants of the variety. It is natural to ask if the constants appearing in some other arithmetic counting results, like counting elliptic curves of bounded naive or Faltings height or counting Galois extensions with fixed Galois group G of bounded discriminant, could be explained in a similar way. But these objects are not parametrized by a variety but by an algebraic stack. In this talk, we will be focused on weighted projective stacks (the stacky quotients (A^n-{0})/Gm for a weighted action), when a complete theory of Manin-Peyre conjecture can be provided. This explains all the constants for the elliptic curves and some of the constants when G=\mu_m is the group of m-th roots of unity.

number theory

Audience: researchers in the topic

Japan Europe Number Theory Exchange Seminar

Series comments: The purpose of the Japan Europe Number Theory Exchange Seminar is to give a opportunity for researchers in Japan and Europe to exchange their research projects by giving short talks (30 min). The target audience are researchers of any level in the area of number theory.

Start for Fall 2021: 26th October