I am currently self-studying elliptic curves using Silverman's AEC. I find his treatment of the background on varieties quite sloppy , and have so far kept going back and forth between AEC and Chapter 1 of Hartshorne, however having to translate between the 2, since their definitions are not identical. Is there an alternative?
2026-03-31 10:08:41.1774951721
Foundations in Silverman's "Arithmetic of Elliptic Curves"
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If it is just about varieties, you could give Mumford‘s Red Book a chance. There also is Garrity‘s Algebraic Geometry A problem solving approach a friend of mine is very fond of. Personally I can recommend Hulek‘s Elementary Algebraic Geometry