Arithmetic volumes of unitary Shimura varieties
NUMBER THEORY
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November 17, 2021 3:00 pm - 4:00 pm
Science Center 507
Address:
1 Oxford Street, Cambridge, MA 02138 USA
Speaker:
Benjamin Howard - Boston College
The integral model of a GU(n-1,1) Shimura variety carries a natural metrized line bundle of modular forms. Viewing this metrized line bundle as a class in the codimension one arithmetic Chow group, one can define its arithmetic volume as an iterated self-intersection. We will show that this volume can be expressed in terms of logarithmic derivatives of Dirichlet L-functions at integer points, and explain the connection with the arithmetic Siegel-Weil conjecture of Kudla-Rapoport. This is joint work with Jan Bruinier.