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I am curious about learning about Abelian varieties, specifically how they are in some ways generalizations of elliptic curves.

I know of the two sources: https://www.jmilne.org/math/CourseNotes/AV.pdf and Abelian varieties by Serge Lang.

Are there others? Which is the best for the viewpoint expressed above?

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    $\begingroup$ There's also Mumford. $\endgroup$
    – Wojowu
    Commented Dec 22, 2021 at 17:08
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    $\begingroup$ This book project van-der-geer.nl/~gerard/AV.pdf by Edixhoven, van der Geer and Moonen looks promising. $\endgroup$
    – Chris Wuthrich
    Commented Dec 22, 2021 at 17:27
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    $\begingroup$ Mumford's Tata Lectures, especially volumes 1 and 3 were excellent references. Mumford also had a little red book, with alot of characteristic p, which i never used. But the Tata lectures had the most detail concerning the different linear algebraic descriptions of "abelian variety". I studied them as symplectic lattices, flat 2g-dimensional real tori with symplectic and complex structures parameterized by Riemann Conditions and Siegel Upper Half space. $\endgroup$
    – JHM
    Commented Dec 22, 2021 at 17:28
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    $\begingroup$ If you're interested in an informal and arithmetically oriented introduction, I can recommend Davide Lombardo's notes: people.dm.unipi.it/lombardo/Teaching/VarietaAbeliane1718/… $\endgroup$
    – Jef
    Commented Dec 22, 2021 at 20:17
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    $\begingroup$ Mumford is the classic, of course. For a first introduction, Bhatt's notes are also pretty good; they use a more up to date language. $\endgroup$
    – R. van Dobben de Bruyn
    Commented Dec 22, 2021 at 21:56

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