A new and complete treatment of semi-abelian degenerations of abelian varieties, and their application to the construction of arithmetic compactifications of Siegel moduli space, with most of the results being published for the first time. Highlights of the book include a classification of semi-abelian schemes, construction of the toroidal and the minimal compactification over the integers, heights for abelian varieties over number fields, and Eichler integrals in several variables, together with a new approach to Siegel modular forms. A valuable source of reference for researchers and graduate students interested in algebraic geometry, Shimura varieties or diophantine geometry.
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First Sentence:
1. Abelian Schemes and Polarizations Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
arithmetic toroidal compactification, rational polyhedral cone decomposition, abelian generic fibre, degeneration data, totally degenerate case, universal abelian variety, complex analytic stack, principally polarized abelian scheme, admissible polyhedral cone decomposition, good algebraic models, universal abelian scheme, strata parametrized, polarized abelian schemes, complex uniformization, conical complex, polyhedral cone decompositions, toral part, dual abelian scheme, minimal compactification, relatively complete models, dense open subscheme, ample invertible sheaf, degenerating abelian varieties, formal cohomology, formal torus Key Phrases - Capitalized Phrases (CAPs): (learn more)
Gluing Good Algebraic Models, Construction of Local Charts, Degeneration of Polarized Abelian Varities, Deligne's Hodge New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
1. Abelian Schemes and Polarizations Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
arithmetic toroidal compactification, rational polyhedral cone decomposition, abelian generic fibre, degeneration data, totally degenerate case, universal abelian variety, complex analytic stack, principally polarized abelian scheme, admissible polyhedral cone decomposition, good algebraic models, universal abelian scheme, strata parametrized, polarized abelian schemes, complex uniformization, conical complex, polyhedral cone decompositions, toral part, dual abelian scheme, minimal compactification, relatively complete models, dense open subscheme, ample invertible sheaf, degenerating abelian varieties, formal cohomology, formal torus Key Phrases - Capitalized Phrases (CAPs): (learn more)
Gluing Good Algebraic Models, Construction of Local Charts, Degeneration of Polarized Abelian Varities, Deligne's Hodge New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 16
books:
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9
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- Abelian Varieties (Tata Institute of Fundamental Research, Bombay// Studies in Mathematics) by David Mumford on page 14, and Back Matter
- Intersection Theory, 2nd Edition by William Fulton in Back Matter (1), and Back Matter (2)
- Hilbert Modular Surfaces (Ergebnisse Der Mathematik Und Ihrer Grenzgebiete 3 Folge) by Gerard Van Der Geer in Back Matter
- Ergodic Theory (Cambridge Studies in Advanced Mathematics) by Karl E. Petersen in Back Matter
- Around Burnside (Ergebnisse Der Mathematik Und Ihrer Grenzgebiete 3 Folge) by A. I. Kostrikin in Back Matter
See all 16 books this book cites
- Geometric Aspects Of Dwork Theory (De Gruyter Proceedings in Mathematics) by Francesco Baldassarri on page 59, and page 227
- Arithmetic Geometry (Symposia Mathematica) by Fabrizio Catanese on page 168
- Abelian Varieties, Theta Functions and the Fourier Transform (Cambridge Tracts in Mathematics) by Alexander Polishchuk in Back Matter
- Moduli Spaces of Abelian Surfaces: Compactification, Degenerations, and Theta Functions (De Gruyter Expositions in Mathematics) by Klaus Hulek in Back Matter
- p-Adic Automorphic Forms on Shimura Varieties (Springer Monographs in Mathematics) by Haruzo Hida in Back Matter
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