Title: Class number formulae for some Shimura varieties of low dimension
Speaker: Shrenik Shah
Speaker Info: Columbia University
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Special Note:
Abstract:
The class number formula connects the residue of the Dedekind zeta function at s=1 to the regulator, which measures the covolume of the lattice generated by logarithms of units. Beilinson defined a generalized regulator morphism and conjectural class number formula in the "motivic" setting. His formula provides arithmetic meaning to the orders of "trivial" zeroes of L-functions at integer points as well as the value of the first nonzero derivative at these points. We study this conjecture for the middle degree cohomology of the Shimura varieties associated to unitary groups of signature (2,1) and (2,2) over Q. We construct explicit "Beilinson-Flach elements" in the motivic cohomology of these varieties and compute their regulator. This is joint work with Aaron Pollack.Date: Monday, January 8, 2018