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I would like to study algebraic geometry and arithmetic curves on my own but are there suggestions where to start? Namely, I like very rigorous way to do mathematics and I was suggested Liu's book "Algebraic Geometry and Arithmetic Curves". But I found it not so well written because for example in exercise 1.1.2 he didn't say what he means by $A$, there are many issues on errata, and I think there are hyphenation problems in the book. For example on page viii there is a wrong hyphenation concern-ing.

Davood Karimi
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wannaberigorous
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  • See this: http://math.stackexchange.com/questions/998/best-algebraic-geometry-text-book-other-than-hartshorne – KittyL Jan 09 '15 at 17:34
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    The paperback edition of Liu's book has a lot of these corrections. And many authors don't maintain errata as Liu does. Hyphenation is probably the least of your problems in life! As far as being expedient, self-contained, and geared toward arithmetic applications I'm not sure that you're going to find anything better. – Hoot Jan 09 '15 at 17:37
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    Anyway, one book you might want to take a look at is Bosch's Algebraic Geometry and Commutative Algebra. – Hoot Jan 09 '15 at 19:00

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