Theory of Degeneration for Polarized Abelian Schemes

In this chapter we reproduce the theory of degeneration data for abelian varieties, following Mumford’s original paper [105] and the first three chapters of Faltings and Chai’s monograph [46]. Although there is essentially nothing new in this chapter, some modifications have been introduced to make...

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Bibliographic Details
Published inArithmetic Compactifications of PEL-Type Shimura Varieties pp. 175 - 284
Main Author Lan, Kai-Wen
Format Book Chapter
LanguageEnglish
Published United States Princeton University Press 21.03.2013
Subjects
Abstract algebra
Algebra
Algebraic geometry
Category theory
Geometry
Homomorphisms
Mathematics
Morphisms
Pure mathematics
Topology
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ISBN9780691156545
0691156549
DOI10.1515/9781400846016.175

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Summary:In this chapter we reproduce the theory of degeneration data for abelian varieties, following Mumford’s original paper [105] and the first three chapters of Faltings and Chai’s monograph [46]. Although there is essentially nothing new in this chapter, some modifications have been introduced to make the statements compatible with our understanding of the proofs. Moreover, since [105] and [46] have supplied full details only in the completely degenerate case, we will balance the literature by avoiding the special case and treating all cases equally. The main objective in this chapter will be to state and prove Theorems 4.2.1.14, 4.4.16, and
ISBN:9780691156545
0691156549
DOI:10.1515/9781400846016.175