Generalized Heegner Cycles, Shimura Curves, and Special Values of p-ADIC L-Functions.

Algebraic Number Theory;Mathematics;Science;Mathematics

Brooks, Ernest HunterLiu, Ruochuan ;

University of Michigan

关键词: Algebraic Number Theory;    Mathematics;    Science;    Mathematics;   

Others  :  https://deepblue.lib.umich.edu/bitstream/handle/2027.42/99928/ehbrooks_1.pdf?sequence=1&isAllowed=y

瑞士|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

We construct ;;generalized Heegner cycles;; on a variety fibered over a Shimura curve, defined over a number field. We show that their images under the p-adic Abel-Jacobi map coincide with the values (outside the range of interpolation) of a p-adic L-function which interpolates special values of the Rankin-Selberg convolution of a fixed newform f and a theta-series attached to an unramified Hecke character of an imaginary quadratic field. This generalizes previous work of Bertolini, Darmon, and Prasanna, which demonstrated a similar result in the case of modular curves. Our main tool is the theory of Serre-Tate coordinates, which yields p-adic expansions of modular forms at CM points, replacing the role of q-expansions in computations on modular curves.