Euler systems and explicit reciprocity laws for GSp(4)

Abstract: Euler systems are a very powerful tool for attacking the Bloch—Kato conjecture, which is one of the central open problems in number theory. In this talk, I will sketch the construction of an Euler system for the spin Galois representation of a genus 2 Siegel modular form. I will then explain how to prove an explicit reciprocity law, relating the image of the Euler system under the Bloch—Kato logarithm map to values of the complex L-function of the Siegel modular form. The applications of this result to the Bloch—Kato conjecture and the Iwasawa Main Conjecture will be discussed by David Loeffler in the following week.

algebraic geometrynumber theory

Audience: researchers in the topic

( slides )

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MIT number theory seminar

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