Canonical Subgroups over Hilbert Modular Varieties
Eyal Z. Goren, Payman L Kassaei
TL;DR
This paper advances the understanding of Hilbert modular varieties in positive characteristic by exploring their geometry and morphisms, and develops a theory of canonical subgroups for abelian varieties with real multiplication using rigid geometry techniques.
Contribution
It introduces new geometric results for Hilbert modular varieties and establishes a novel theory of canonical subgroups in the context of real multiplication.
Findings
New geometric properties of Hilbert modular varieties in positive characteristic
Development of a canonical subgroup theory for abelian varieties with real multiplication
Application of rigid geometry methods to modular variety problems
Abstract
We obtain new results on the geometry of Hilbert modular varieties in positive characteristic and morphisms between them. Using these results and methods of rigid geometry, we develop a theory of canonical subgroups for abelian varieties with real multiplication.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Algebra and Geometry · Geometric and Algebraic Topology