On the integrality of modular symbols and Kato's Euler system for elliptic curves

Abstract

Let $E/\mathbb{Q}$ be an elliptic curve. We investigate the denominator of the modular symbols attached to $E$. We show that one can change the curve in its isogeny class to make these denominators coprime to any given odd prime of semi-stable reduction. This has applications to the integrality of Kato's Euler system and the main conjecture in Iwasawa theory for elliptic curves.