By Kai-Wen Lan
By learning the degeneration of abelian kinds with PEL constructions, this ebook explains the compactifications of soft quintessential types of all PEL-type Shimura kinds, delivering the logical beginning for a number of interesting contemporary advancements. The ebook is designed to be obtainable to graduate scholars who've an realizing of schemes and abelian varieties.
PEL-type Shimura types, that are typical generalizations of modular curves, are valuable for learning the mathematics homes of automorphic kinds and automorphic representations, they usually have performed vital roles within the improvement of the Langlands software. As with modular curves, it's fascinating to have necessary types of compactifications of PEL-type Shimura forms that may be defined in enough element close to the boundary. This booklet explains intimately the subsequent themes approximately PEL-type Shimura forms and their compactifications:
- A building of gentle imperative types of PEL-type Shimura types by means of defining and representing moduli difficulties of abelian schemes with PEL buildings
- An research of the degeneration of abelian types with PEL constructions into semiabelian schemes, over noetherian common entire adic base jewelry
- A building of toroidal and minimum compactifications of soft essential types of PEL-type Shimura forms, with distinct descriptions in their constitution close to the boundary
Through those themes, the ebook generalizes the speculation of degenerations of polarized abelian forms and the appliance of that thought to the development of toroidal and minimum compactifications of Siegel moduli schemes over the integers (as constructed via Mumford, Faltings, and Chai).
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Arithmetic Compactifications of PEL-Type Shimura Varieties (London Mathematical Society Monographs) by Kai-Wen Lan