Arithmetic volumes of unitary Shimura varieties


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November 17, 2021 3:00 pm - 4:00 pm
Science Center 507
Address: 1 Oxford Street, Cambridge, MA 02138 USA

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.