Periods of Quaternionic Shimura Varieties. I.

Häftad, Engelska, 2021

1 859 kr

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This book formulates a new conjecture about quadratic periods of automorphic forms on quaternion algebras, which is an integral refinement of Shimura's algebraicity conjectures on these periods. It also provides a strategy to attack this conjecture by reformulating it in terms of integrality properties of the theta correspondence for quaternionic unitary groups. The methods and constructions of the book are expected to have applications to other problems related to periods, such as the Bloch-Beilinson conjecture about special values of $L$-functions and constructing geometric realizations of Langlands functoriality for automorphic forms on quaternion algebras.

Produktinformation

Utgivningsdatum2021-03-30
Mått178 x 254 x undefined mm
Vikt395 g
FormatHäftad
SpråkEngelska
SerieContemporary Mathematics
Antal sidor220
FörlagAmerican Mathematical Society
ISBN9781470448943

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Matematik inom Naturvetenskap och teknik

IntroductionQuaternionic Shimura VarietiesUnitary and Quaternionic Unitary GroupsWeil RepresentationsThe Rallis Inner Product Formula and the Jacquet-Langlands Correspondence Schwartz FunctionsExplicit Form of the Rallis Inner Product FormulaThe Main Conjecture on the Arithmetic of Theta LiftsAppendix A. Abelian Varieties, Polarizations and Hermitian Forms Appendix B. Metaplectic Covers of Symplectic Similitude Groups Appendix C. Splittings: The Case $\textrm{dim}_{B}V =2$ and $\textrm{dim}_{B}W =1$Appendix D. Splittings for the Doubling Method: Quaternionic Unitary Groups Bibliography