961 research outputs found
CM cycles on Shimura curves, and p-adic L-functions
Let f be a modular form of weight k>=2 and level N, let K be a quadratic
imaginary field, and assume that there is a prime p exactly dividing N. Under
certain arithmetic conditions on the level and the field K, one can attach to
this data a p-adic L-function L_p(f,K,s), as done by
Bertolini-Darmon-Iovita-Spiess. In the case of p being inert in K, this
analytic function of a p-adic variable s vanishes in the critical range
s=1,...,k-1, and therefore one is interested in the values of its derivative in
this range. We construct, for k>=4, a Chow motive endowed with a distinguished
collection of algebraic cycles which encode these values, via the p-adic
Abel-Jacobi map.
Our main result generalizes the result obtained by Iovita-Spiess, which gives
a similar formula for the central value s=k/2. Even in this case our
construction is different from the one found by Iovita-Spiess
- …