Special cohomology classes for modular Galois representations

✍ Scribed by Benjamin Howard

• Publisher: Elsevier Science
• Year: 2006
• Tongue: English
• Weight: 344 KB
• Volume: 117
• Category: Article
• ISSN: 0022-314X
• DOI: 10.1016/j.jnt.2005.07.002

✦ Synopsis

Building on ideas of Vatsal [Uniform distribution of Heegner points, Invent. Math. 148(1) (2002) 1-46], Cornut [Mazur's conjecture on higher Heegner points, Invent. Math. 148(3) (2002) 495-523] proved a conjecture of Mazur asserting the generic nonvanishing of Heegner points on an elliptic curve E /Q 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 two-dimensional -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.