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Euler Systems seminar

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.



Speaker Date Talk
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