# Arithmetic transfer conjectures for unitary groups

## Brian Smithling, Johns Hopkins

The arithmetic fundamental lemma is a conjectural relation proposed by W. Zhang in connection with a relative trace formula approach to the hermitian case of the arithmetic Gan-Gross-Prasad conjecture. It asserts a deep relation between the derivative of an orbital integral and an intersection number for cycles in a formal moduli space of p-divisible groups attached to an unramified unitary group over a p-adic field. I will report on some extensions of the AFL conjecture to settings in which the unitary group is ramified, and in cases of low rank their proof. This is joint work with M. Rapoport and W. Zhang.

Tuesday, September 1st, at 4:00pm in HBH 227

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