Institut für MathematikHome > Academic programme > Seminars & Colloquia > Oberseminar: Algebraische Geometrie > Kudla's modularity conjecture and formal Fourier-Jacobi series

  Deutsch  |  Contact  |  Print  |  Search  

FÜR SCHÜLERiNNEN
INSTITUTE
ACADEMIC PROGRAMME
COLLOQUIA/SEMINARS
STUDENT SEMINARS
LECTURE COURSES
MODULES
CONFERENCES/EVENTS
VORKURSE
FOR STUDENTS
FOR PhD STUDENTS



Modul:   MAT770  Oberseminar: Algebraische Geometrie


Kudla's modularity conjecture and formal Fourier-Jacobi series

Prof. Dr. Jan Hendrik Bruinier's talk

Date: 16.03.15   Time: 13.15 - 14.45   Room: Y27H25

A famous theorem of Gross, Kohnen, and Zagier states that the generating series of Heegner divisors on a modular curve is an elliptic modular form of weight 3/2 with values in the Picard group. This result can be viewed as an elegant description of the relations among Heegner divisors. More generally, Kudla conjectured that the generating series of codimension g special cycles on an orthogonal Shimura variety of dimension n is a Siegel modular form of genus g and weight 1+n/2 with coefficients in the Chow group of codimension g cycles. We report on joint work with Martin Westerholt-Raum on the modularity of formal Fourier-Jacobi series, which, when combined with a result of Wei Zhang, leads to a proof of Kudla's modularity conjecture.