This research extends a formula for arithmetic degree in CM elliptic curves, indicating new insights into QM abelian surfaces.
In this paper we generalize a theorem of Kudla-Rapoport-Yang which gives a formula for the arithmetic degree of the moduli space of CM elliptic curves together with a special endomorphism of a specified degree. Our extension is to the moduli space of QM abelian surfaces with CM together with a special endomorphism of a specified QM degree.
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Andrew Phillips (2025) studied this question.
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