Shimura subvarieties via endomorphisms
Irene Spelta
TL;DR
This paper constructs new Shimura subvarieties within moduli spaces of abelian varieties, using Jacobians with special endomorphisms, expanding the understanding of their geometric and arithmetic properties.
Contribution
It introduces the first examples of Shimura subvarieties derived from Jacobians with non-trivial endomorphisms not stemming from curve automorphisms.
Findings
Two new Shimura subvarieties in _2 and _3 within the Torelli locus.
A new Shimura subvariety in _4 within the Prym locus.
These subvarieties are characterized by Jacobians with special endomorphisms.
Abstract
We show the existence of two new Shimura subvarieties of generically contained in the Torelli locus. They provide the first examples of Shimura subvarieties obtained by means of Jacobians carrying non-trivial endomorphisms not directly induced by the automorphisms of the curves. We also obtain a new example of a Shimura subvariety of generically contained in the Prym locus.
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Taxonomy
TopicsCarbohydrate Chemistry and Synthesis · Advanced Differential Equations and Dynamical Systems · Alzheimer's disease research and treatments