253 research outputs found
Definability of restricted theta functions and families of abelian varieties
We consider some classical maps from the theory of abelian varieties and
their moduli spaces and prove their definability, on restricted domains, in the
o-minimal structure \Rae. In particular, we prove that the embedding of
moduli space of principally polarized ableian varierty, Sp(2g,\Z)\backslash
\CH_g, is definable in \Rae, when restricted to Siegel's fundamental set
\fF_g. We also prove the definability, on appropriate domains, of embeddings
of families of abelian varieties into projective space
Ax-Schanuel for Shimura varieties
We prove the Ax-Schanuel theorem for a general (pure) Shimura variety
Hyperbolic Ax-Lindemann theorem in the cocompact case
We prove an analogue of the classical Ax-Lindemann theorem in the context of
compact Shimura varieties. Our work is motivated by J. Pila's strategy for
proving the Andr\'e-Oort conjecture unconditionallyComment: To appear in Duke Mathematical Journa
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