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A generalisation of Heegner Points?

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Let K be a CM field with totally real subfield F. Let M be a motive over F with coefficients in a number field C. Suppose that M is symplectic and pure of weight -1.

In some cases, the Bloch-Kato conjectures and global sign considerations suggest that there should exist an Euler System for M over K. Under some further assumptions (automorphicity and behavior of M at the archimedean places), conjectures of Langlands, Vogan, Arthur and local sign considerations suggest the construction of (a candidate for) such an Euler system. For M = h^1(E)(1) with E an elliptic curve over F = Q, the whole process yields just the classical Euler system of Heegner points.

This talk is part of the Number Theory Seminar series.

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