University of Arizona
When
2 – 3 p.m., March 25, 2025
Where
Title: Gross lattices of supersingular elliptic curves
Abstract: Chevyrev and Galbraith (2013) and Goren and Love (2023) show that the successive minima of the Gross lattice of a supersingular elliptic curve can be used to characterize the endomorphism ring of that curve. We show that the third successive minimum D3 of the Gross lattice gives necessary and sufficient conditions for the curve to be defined over the field Fp or over the field Fp2. In the case where the curve E is defined over Fp, the value of D3 can even yield finer information about the endomorphism ring of E. This talk is based on my joint work with Chenfeng He, Ha Tran, and Christelle Vincent.