Speaker: Lynnelle Ye

Title: Euler systems and the Main Conjecture

Abstract: We will explain the use of Euler systems in the proof of the Main Conjecture. To this end, we will first review the motivation and statement of the Main Conjecture. Then we will give a high-level summary of how Euler systems arise when one tries to prove the Main Conjecture (more details will be given in future weeks), and, consequently, why we need the Factorization Theorem along with a lemma about ideal class representatives in the proof. Finally, we will prove the Factorization Theorem and the additional lemma.