MIT Number Theory Seminar
Tuesday, November 13, 2018 at 4:30pm to 5:30pm
2-143
Daniel Kriz (MIT)
Title: “A new p-adic Maass-Shimura operator and supersingular Rankin-Selberg p-adic L-functions”
Abstract: We introduce a new p-adic Maass–Shimura operator acting on a space of “generalized p-adic modular forms” (extending Katz’s notion of p-adic modular forms), defined on the p-adic (preperfectoid) universal cover of a Shimura curve. Using this operator, we construct new p-adic L-functions in the style of Katz, Bertolini–Darmon–Prasanna and Liu–Zhang–Zhang for Rankin–Selberg families over imaginary quadratic fields K, in the ”supersingular” case where p is inert or ramified in K. We also establish new p-adic Waldspurger formulas, relating p-adic logarithms of elliptic units and Heegner points to special values of these p-adic L-functions. If time permits, we will discuss some applications to the arithmetic of abelian varieties.
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