Delta-Invariant Theory for Hecke Correspondences
Buch in deiner Nähe kaufen
Beschreibung
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.
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.
Introduces the new field of δ-geometry Provides applications to the construction of quotient spaces that do not exist in usual algebraic geometry Gives an in-depth study of the invariant theory of tuples of quadrics
Autor*in
Alexandru Buium
Themen in »Delta-Invariant Theory for Hecke Correspondences«
abelian schemes cohomology field geometric invariant theory Fermat quotients flow Fourier expansion group scheme Hecke correspondences Hecke covariant form Hilbert series modular form quadrics invariant quasi-linearity quotient