Compactification of the Drinfeld Modular Surfaces

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In this article the author describes in detail a compactification of the moduli schemes representing Drinfeld modules of rank 2 endowed with some level structure. The boundary is a union of copies of moduli schemes for Drinfeld modules of rank I, and its points are interpreted as Tate data. The author also studies infinitesimal deformations of Drinfeld modules with level structure.