Derived special cycles on Shimura varieties

Abstract: We employ methods from derived algebraic geometry to give a uniform moduli-theoretic construction of special cycle classes on many Shimura varieties of Hodge type. Our results apply in particular to classes on GSpin Shimura varieties associated with arbitrary positive semi-definite symmetric matrices, as well as to certain unitary and quaternionic Shimura varieties. We show that these classes agree with the ones constructed in work with B. Howard using $K$-theoretic methods.

algebraic geometrynumber theory

Audience: researchers in the topic

MIT number theory seminar

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