Counting “supersingularity” in arithmetic statistics

Wanlin Li

Supersingularity is a notion to describe certain elliptic curves defined over a field with positive characteristic $p > 0$. Supersingular elliptic curves possess many special properties, such as larger endomorphism rings, extremal point counts, and special p-torsion group scheme structures. This notion was then generalized to higherdimensional abelian varieties. A global function field is associated with an algebraic curve defined over a finite field; the supersingularity of the Jacobian would affect the prime distribution of this function field. In this talk, I want to discuss the effect of supersingularity on prime distribution for function fields and introduce some perspectives to study this phenomenon.

https://mathtube.org/lecture/video/counting-%E2%80%9Csupersingularity%E2%80%9D-arithmetic-statistics

Mathtube- Comparative Prime Number Theory