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Do you have interesting books presenting abelian variety (over an arbitrary field k) using the scheme point of view? Most of the lectures I know use the point of view presented in the first chapter of Hartshorne (so without scheme).

I'm looking for something which presents the modern aspects/questions of those objects.

Analyse300
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  • See Milne, Abelian varieties. There will probably be some new materials in a few months, after the Arizona Winter School. See also a book (project?) by Edixhoven, van der Geer and Moonen eg here: http://van-der-geer.nl/~gerard/AV.pdf . – Aphelli Oct 07 '23 at 09:01
  • Wow : the book of van der Geer and Moonen is great. That's what I was looking for!!! – Analyse300 Oct 07 '23 at 10:46
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    To add to Aphelli's answer, there is also Mumford's Abelian Varieties (middle of the book on onwards), and Polishchuk's Abelian Varieties, Theta Functions and the Fourier Transform. – Shrugs Nov 21 '23 at 15:41
  • Hello, many thanks to you! – Analyse300 Nov 22 '23 at 17:47

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