On the Mod p Iwasawa Theory for Elliptic Curves

In this note, we study the mod p behavior of Kato’s Euler systems and fine Selmer groups for an elliptic curve with good reduction at a prime \(p \ge 5\) . We show that we observe a version of the \(\lambda \) -invariant formula for fine Selmer groups for congruent elliptic curves holds, as in the work of Greenberg–Vatsal, and formulate a mod p version of Kato’s main conjecture.