Non vanishing of Hecke L values
DOI:
https://doi.org/10.51094/jxiv.902Keywords:
Hecke L-valus, Mordel-Weil rankAbstract
Following the research by Rohrich and Lamplugh, the non-vanishing of -values has been extensively studied. In Theorem A, we extend Lamplugh's results on -values obtained for imaginary quadratic fields to CM fields. The key ingredient is the equivariant cohomology class on Poincare sheaf, the so-called Eisenstein-Kronecker class constructed by G. Kings and J. Sprang in 2019. This allows us to connect the transcendence of formal functions to the study of -values. In Theorem B, assuming the BSD conjecture, we show that in a suitable multiple Zl extension , the Z-module X(J)/X(J)tors of a CM-type abelian variety X with good ordinary reduction at all primes above is a finitely generated Z-module. This is an immediate consequence of Theorem A.
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