By Kai-Wen Lan
By learning the degeneration of abelian kinds with PEL constructions, this ebook explains the compactifications of delicate critical versions of all PEL-type Shimura kinds, supplying the logical beginning for numerous 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 forms, that are normal generalizations of modular curves, are invaluable for learning the mathematics houses of automorphic kinds and automorphic representations, they usually have performed very important roles within the improvement of the Langlands software. As with modular curves, it truly is fascinating to have essential types of compactifications of PEL-type Shimura kinds that may be defined in enough aspect close to the boundary. This ebook explains intimately the subsequent themes approximately PEL-type Shimura types and their compactifications:
- A building of gentle crucial versions of PEL-type Shimura kinds by way of defining and representing moduli difficulties of abelian schemes with PEL buildings
- An research of the degeneration of abelian forms with PEL buildings into semiabelian schemes, over noetherian common whole adic base earrings
- A building of toroidal and minimum compactifications of tender fundamental versions of PEL-type Shimura forms, with unique descriptions in their constitution close to the boundary
Through those subject matters, the e-book generalizes the idea of degenerations of polarized abelian kinds and the appliance of that conception to the development of toroidal and minimum compactifications of Siegel moduli schemes over the integers (as built by means of Mumford, Faltings, and Chai).
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