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Arithmetic Compactifications of PEL-Type Shimura Varieties$
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Kai-Wen Lan

Print publication date: 2013

Print ISBN-13: 9780691156545

Published to Princeton Scholarship Online: October 2017

DOI: 10.23943/princeton/9780691156545.001.0001

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Theory of Degeneration for Polarized Abelian Schemes

Theory of Degeneration for Polarized Abelian Schemes

(p.175) Chapter Four Theory of Degeneration for Polarized Abelian Schemes
Arithmetic Compactifications of PEL-Type Shimura Varieties

Kai-Wen Lan

Princeton University Press

This chapter reproduces the theory of degeneration data for polarized abelian varieties, following D. Mumford's 1972 monograph, An analytic construction of degenerating abelian varieties over complete rings, as well as the first three chapters of the Degeneration of abelian varieties (1990), by G. Faltings and C.-L. Chai. Although there is essentially nothing new in this chapter, some modifications have been introduced to make the statements compatible with a certain understanding of the proofs. Moreover, since Mumford and Faltings and Chai have supplied full details only in the completely degenerate case, this chapter balances the literature by avoiding the special case and treating all cases equally.

Keywords:   polarized abelian schemes, degeneration data, polarized abelian varieties, degeneration data

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