Hilbert modular surfaces, Hirzebruch-Zagier cycles and a p-adic Gross-Zagier formula for Hilbert modular forms
Speaker: Iván Blanco Chacón (UCD)
Date: Monday, 28th September 2015
Time: 4pm – 5pm
Location: Agriculture. 1.01 (Seminar Room).
Abstract:
We explain our recent joint work with Ignacio Sols, in which we solve a question posed by Henri Darmon in 2014. For a rational elliptic curve of conductor N_1, we consider the attached cuspform provided by the modularity theorem. The modular curve is generically embedded in the Hilbert modular surface of level one. We consider a level N_2 > 3 so that the corresponding Hilbert modular surface is a fine moduli space of HBAS. Choosing a suitable prime p, by the use of recent work of Hida, we construct a 2-variable p-adic L-function whose special values interpolates the p-adic Abel jacobi map at a Hirzebruch-Zagier cycle. Our intention is to construct non-geometrical Euler-Kato systems in the elliptic curve, non-reachable by modular or Shimura parametrisations.
Series: Algebra and Number Theory
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