5 papers
Computing endomorphism rings of supersingular elliptic curves and connections to pathfinding in isogeny graphs
Kirsten Eisentraeger, Sean Hallgren, Chris Leonardi +2
Computing endomorphism rings of supersingular elliptic curves is an important problem in computational number theory, and it is also closely connected to the security of some of th…
Everywhere local solubility for hypersurfaces in products of projective spaces
Tom Fisher, Wei Ho, Jennifer Park
We prove that a positive proportion of hypersurfaces in products of projective spaces over are everywhere locally soluble, for almost all multidegrees and dimensions,…
Cycles in the supersingular -isogeny graph and corresponding endomorphisms
Efrat Bank, Catalina Camacho-Navarro, Kirsten Eisentraeger +2
We study the problem of generating the endomorphism ring of a supersingular elliptic curve by two cycles in -isogeny graphs. We prove a necessary and sufficient condition for…
Effective Chabauty for symmetric powers of curves
Jennifer Park
Faltings' theorem states that curves of genus have finitely many rational points. Using the ideas of Faltings, Mumford, Parshin and Raynaud, one obtains an upper bound o…
Comparing arithmetic intersection formulas for denominators of Igusa class polynomials
Jacqueline Anderson, Jennifer S. Balakrishnan, Kristin Lauter +2
Bruinier and Yang conjectured a formula for intersection numbers on an arithmetic Hilbert modular surface, and as a consequence obtained a conjectural formula for CM(K).G_1 under s…