|Location:||MSRI: Simons Auditorium, Online/Virtual|
We will construct Sharifi's "Upsilon map", which is a map from the ideal class group side to the modular symbol side, and it is the conjectural inverse to the evaluation at infinity map. This involves understanding the big ordinary Galois representation modulo the Eisenstein ideal. Anticipating the result of Fukaya--Kato to be covered in the third talk, we explain how the Upsilon map can be regarded as a connecting map between Galois cohomology groups.
Study on Sharifi's Conjecture
Sharifi's Conjecture II: The Upsilon Map