This is the webpage for the Euler Systems learning seminar taking place online via Zoom every Friday at 3pm UK time /4pm CET . In this seminar, we will study three classical examples of Euler systems along with their applications to various important problems in number theory:
- Cyclotomic units and their application to Iwasawa theory (due to Thaine, Kolyvagin and Rubin).
- Elliptic units and their application to BSD in analytic rank zero for CM elliptic curves (due to Coates and Wiles).
- Heegner points and their application to proving BSD and finiteness of the Tate—Shafarevich group in analytic rank <= 1 (due to Gross-Zagier and Kolyvagin).
The detailed program (along with references) can be found here.
|Arshay Sheth||28th July||Introduction|
|Muhammad Manji||4th August||Cyclotomic units and applications to Iwasawa theory|
|Khai Hoan Nguyen Dang||11th August||Background on Selmer groups|
|Adithya Chakravarthi||18th August||The Euler system of elliptic units|
|Khai Hoan Nguyen Dang||25th August||Bounding the ideal class group of K(E[p])|
|Robin Visser||1st September||Elliptic units and L-functions of elliptic curves|
|Wojtek Wawrow||8th September||Proof of the Coates--Wiles theorem|
|Ana Marija Vego||15th September||Heegner Points|
|Arshay Sheth||22nd September||Kolyvagin's derived classes|
|Elie Studnia||29th September||Proof of Kolyvagin's theorem|