Arithmetic Geometry
Varieties over number fields, etale cohomology, and Diophantine geometry.
Arithmetic Geometry. Varieties over number fields, etale cohomology, and Diophantine geometry.
Foundations and canonical references
The standard treatments of arithmetic geometry approach the subject from complementary angles. Silverman, Arithmetic of Elliptic Curves (2009) is the anchor reference for the subject and lays out the core definitions, theorems, and worked examples that practitioners return to. Neukirch, Algebraic Number Theory (1999) gives a parallel, more proof-oriented exposition of the same material and is widely used as a graduate text.
Open methodological questions for arithmetic geometry 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 · 2009Arithmetic of Elliptic Curvessilverman-2009
- textbook · primary · 1999Algebraic Number Theoryneukirch-1999
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