29th November: Dingli Liang

Title: Non-commutative Iwasawa theory and GL_2 main conjecture for elliptic curves without complex multiplication

Abstract: In this talk, first we will recall the classical Iwasawa theory for number field and elliptic curves, to explain the motivation for non-commutative Iwasawa theory. And then we will recall "the five guys" famous work, which identify a proper category to fomulate a main conjecture for elliptic curves without multiplication. This work combines non-commutative algebra and algebraic K theory to define a characteristic elements in K_1, perfectly describing the p-adic L-function in this case. And also, as a important tool, akashi series plays a leading role in the statement of the well-defined proposition of characteristic element.