Special cohomology classes for modular Galois representations

Benjamin Howard

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arXiv · 1202.6355

Special cohomology classes for modular Galois representations

Benjamin Howard

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Abstract

Building on ideas of Vatsal, Cornut proved a conjecture of Mazur asserting the generic nonvanishing of Heegner points on an elliptic curve E as one ascends the anticyclotomic Z_p-extension of a quadratic imaginary extension K/Q. In the present article Cornut's result is extended by replacing the elliptic curve E with the Galois cohomology of Deligne's 2-dimensional l-adic representation attached to a modular form of weight 2k>2, and replacing the family of Heegner points with an analogous family of special cohomology classes.

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Benjamin Howard. 2012-02-28. Special cohomology classes for modular Galois representations. https://arxiv.org/abs/1202.6355

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