Description
Abstract: I will discuss the factorization of a certain triple product p-adic L-function whose interpolation range is empty. The relevant factorization statement reflects the Artin formalism for the underlying family of motives (that decompose as the sum of 2 motives of respective degrees 2 and 6). I will explain how this can be recast in terms of the interplay between cycles that are governed by the Gross--Zagier and (conjectural) Gross--Kudla--Schoen formulae for the relevant complex L-series.
The statement of this conjecture was conceived through calculations with Jan's interpretation of algebraic p-adic L-functions (as determinants of Selmer complexes). One unconditional evidence towards this conjecture is the verification of its algebraic counterpart that is formulated in terms of these.
