On the Integrality of Modular Symbols and Kato's Euler System for Elliptic Curves

Let $E/\QQ$ 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.

2010 Mathematics Subject Classification: 11G05, 11F67, 11G40, 11R23, 11G16.

Keywords and Phrases: Elliptic Curves, modular symbols, Kato's Euler system

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