Kato’s Euler system
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Venerucci’s proof of the Mazur-Tate-Teitelbum conjecture in rank 1
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Kolyvagin’s Theorem I
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Kolyvagin’s Theorem II
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Diagonal cycles
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Cohomological interpretation of L-values
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On the exceptional zeros of p-adic L-functions of Hilbert modular forms
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The use of modular symbols to attach p-adic Lfunctions to Hecke eigenforms goes back to the work of Manin et al in the 70s.
Euler Systems – Introduction
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We will start looking at the second part of “L-functions and Euler systems: a tale in two trilogies” (available at http://www.math.mcgill.ca/darmon/pub/Articles/Research/61.Durham-ES/durham.pdf), and distributing talks.
Triple product p-adic L-functions and iterated integrals
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I will explain A.Lauder’s approach to computing special values of Rankin triple product p-adic L-functions. These have quite striking applications to the arithmetic of elliptic curves, and appear in the “Elliptic Stark Conjecture” of Darmon-Lauder-Rotger.
Hida-Rankin p-adic L-function
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Second talk of the learning seminar on the Tale on 2 trilogies.