This book presents a complete treatment of semi-abelian degenerations of abelian varieties, and their application to the construction of arithmetic compactifications of Siegel moduli space. Most results are new and have never been published before. Highlights of the book include a classification of semi-abelian schemes, construction of the ...
The arithmetic Riemann-Roch theorem has been shown recently by Bismut-Gillet-Soule. The proof mixes algebra, arithmetic and analysis. The purpose of this book is to give a concise introduction to the necessary techniques, and to present a simplified and extended version of the proof. It should enable mathematicians with a background in ...
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