The Tate Conjectures for Hilbert Modular Surfaces
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Once one has models for Hilbert modular varieties over (rings of integers of) number fields one can start investigating the arithmetic properties of Hilbert modular varieties. The wealth of results (and conjectures) for the moduli spaces of elliptic curves suggests that unexpected treasures lie buried in a largely unexplored territory.
KeywordsModular Form Galois Representation Automorphic Representation Algebraic Cycle Compact Open Subgroup
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