Norm relations for CM points on modular curves

2023/10/23 by Shah, Syed Waqar Ali
#11G18 #11R23 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2310.14543

Abstract

Kolyvagin introduced the method of Euler systems to study the structure of Selmer groups of elliptic curves. In this semi-expository article, we prove the horizontal norm relations for the CM points on modular curves underlying Kolyvagin's Euler system, with a view toward higher-dimensional generalizations.

Related

• Euler systems of K₂ of CM elliptic curves
• Kolyvagin systems of rank 0 and the structure of the Selmer group of elliptic curves over abelian extensions
• A higher Gross-Zagier formula and the structure of Selmer groups
• The structure of Selmer groups of elliptic curves and modular symbols
• Kolyvagin's Conjecture and patched Euler systems in anticyclotomic Iwasawa theory