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Iwasawa theory, special values of L-functions, and regulators, I.

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KAH - K-theory, algebraic cycles and motivic homotopy theory

I will give a brief introduction to some of the conjectures relating special values of L-functions to regulators of motivic cohomology classes, such as Beilinson's conjecture and the Bloch-Kato conjecture. I will then describe the p-adic 'mirror image' of these conjectures proposed by Perrin-Riou, and how the methods of Iwasawa theory can be used to make substantial progress on these p-adic conjectures. I will illustrate this with the examples of the Riemann zeta function and the L-functions of elliptic curves, and some more
recent developments if time allows.

This talk is part of the Isaac Newton Institute Seminar Series series.

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