Arithmetic level raising on triple product of Shimura curves and Gross-Schoen Diagonal cycles I: Ramified case

2020/04/01 by Wang, Haining
#Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2004.00555

Abstract

In this article we study the Gross-Schoen diagonal cycle on a triple product of Shimura curves at a place of bad reduction. We relate the image of the diagonal cycle under the Abel-Jacobi map to certain period integral that governs the central critical value of the Garrett-Rankin type triple product L-function via level raising congruences. As an application we prove certain rank 0 case of the Bloch-Kato conjecture for the symmetric cube motive of a weight 2 modular form.

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