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An Euler-Kolyvagin system machinery of rank r

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For a p-adic Galois representation T, I will devise a general Euler/Kolyvagin system machinery which as an input takes an Euler system of rank r (in the sense of Perrin-Riou), and gives a bound on the Bloch-Kato Selmer group in terms of an r x r determinant. I will give two fundamental applications of this refinement: The first with the (conjectural) Rubin-Stark elements; and the second with Perrin-Riou’s (conjectural) p-adic L-functions.

This talk is part of the Number Theory Seminar series.

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