Counting “supersingularity” in arithmetic statistics

Speaker: Wanlin Li

Date: Tue, Jun 18, 2024

Location: PIMS, University of British Columbia

Conference: Comparative Prime Number Theory

Subject: Mathematics, Number Theory

Class: Scientific

CRG: L-Functions in Analytic Number Theory


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.

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