Injectivity of the Abel-Jacobi map and Gross-Kudla-Schoen cycles

Abstract: On the triple product of a quaternionic Shimura curve over a totally real field, the injectivity of the Abel-Jacobi map implies an automorphic decomposition of the Chow groups. Then Prasad's theorem on trilinear forms implies the vanishing of the isotypic component of the Gross-Kudla-Schoen modified diagonal cycle with a certain local root number. We define such a decomposition unconditionally and prove the vanishing. This is a special case of some general results.

Mathematics

Audience: researchers in the topic

Southern California Number Theory Day

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