|Location:||MSRI: Simons Auditorium, Online/Virtual|
ES Learning Seminar: "Sharifi's Conjecture IV: Odds And Ends And Eisenstein Cocycles"
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I hope to begin with a few observations on how the geometry of modular curves “near the cusps” provides insight into the arithmetic of cyclotomic fields, particularly in terms of the two divisibilities in the Iwasawa main conjecture. I’ll transition from there to describe a construction with A. Venkatesh of a motivic GL_2-cocycle that is “Eisenstein” and pulls back to provide an explicit map taking Manin symbols to certain Steinberg symbols. This construction is set up to be generalizable, and in that vein, I may hint at what analogues of a conjecture of mine should look like.
Sharifi's Conjecture IV