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Abstract: This talk introduces the setting of the Kulda program we will study throughout the rest of the semester: unitary Shimura varieties. Geometrically, unitary Shimura varieties are arithmetic quotients of unit balls which are realizable as the complex points of a quasi-projective algebraic variety. Arithmetically, this variety descends to a variety over a totally real number field. Integrally, certain unions of these varieties represent a moduli problem which has an integral structure.

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