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This book provides an introduction to the new field of δ-geometry and its applications to the construction of certain quotient spaces that cannot be approached within usual algebraic geometry, specifically quotients of Siegel moduli spaces by the action of Hecke correspondences. δ-geometry is a geometry obtained from usual algebraic geometry by ‘adjoining’ a Fermat quotient operator; the latter morally plays the role of an ‘arithmetic differentiation’ with respect to a prime integer. The book assumes some basic knowledge of the algebraic geometry of schemes, including abelian schemes, but it is otherwise self-contained.

Its intended audience includes mathematics graduate students and researchers interested in algebraic geometry and number theory.