Seminar

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We will discuss the method of Fukaya--Kato on conjectures of Sharifi. We give some Galois cohomological understandings of the varpi map and upsilon map constructed in previous talks. For this, we review the Galois structures of the pieces P and Q of H/IH. One main goal is to show the commutativity of the big diagram appearing in the end of last talk. Using some homological algebras and a power series computation, an explicit cup product map is magically identified as the multiplication of the derivative of p-adic Dirichlet L function \zeta’. Combine the commutativity with an analytic relation between \zeta’ and another two-variable p-adic L function, we obtain the main result of Fukaya-Kato. 

Study on Sharifi's Conjecture 135 KB application/pdf