Keerthi Madapusi Pera

Abstract:  I’ll show how methods from derived algebraic geometry can be used to give a very quick construction of cycle classes of all codimensions in the unitary Shimura varieties considered by Kudla and Rapoport. A key point here is that the cycles are defined via loci where one has additional homomorphisms out of a CM elliptic curve (for instance, in the dimension 1 case, one recovers the usual CM cycles on the modular curve). I will then indicate how this can be generalized to other Shimura varieties to which Kudla’s conjectures apply.