I am a foreign master student in algebra at the final year. I'm familar with categorical algebra and have interesting in algebraic geomery and number theory. I have learned some knowledge about scheme theory and algebraic number theory from online notes, but have not read Hartshorne yet.
I want to apply for a Phd program in algebraic geometry or arithmetic geometry in US universities. But I wonder if my background can be accepted, especailly considering my poor english skill.
My questions are:
1, Can my background be accepted for some good Phd programs in algebraic/arithmetic geometry?
2, Except Harvard, Princeton, Berkeley, Chicago, MIT, Stanford, Columbia etc., which have been listed in USNews, where are good Phd programs in algebraic/arithmetic geometry?
3, Is there some useful suggestions about further learning on algebraic/arithmetic geometry?
