Abelian Varieties
Higher-dimensional analogs of elliptic curves and their endomorphism rings.
Abelian Varieties. Higher-dimensional analogs of elliptic curves and their endomorphism rings.
Foundations and canonical references
The standard treatments of abelian varieties approach the subject from complementary angles. Mumford, Abelian Varieties (2008) is the anchor reference for the subject and lays out the core definitions, theorems, and worked examples that practitioners return to.
Open methodological questions for abelian varieties include sharpening the bridges between foundational theory and computational practice, extending classical results to broader or more structured settings, and integrating the techniques surveyed above with adjacent mathematical disciplines. The references listed in this page are the entry points that current work builds on.
Prerequisites
Sources
- textbook · primary · 2008Abelian Varietiesmumford-2008
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