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I am a physics major who's studying mathematics, and I am interested in Topology and Geometry. I am mainly interested in Michael Atiyah's work in Algebraic Geometry and Chern-Simons Theories in physics.

What are the prerequisites in Abstract Algebra and Topology for Algebraic Geometry? I have already taken Real Analysis at Rudin Level, Group, Ring, and Module Theory at Dummit and Foote level. Are Field and Galois theories required to study Algebraic Geometry? Also, would Multivariate Analysis be helpful?

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Question: "Are Field and Galois theories required to study Algebraic Geometry? Also, would Multivariate Analysis be helpful?"

Answer: You should find a good book on field theory and Galois theory, and also read some books on commutative algebra: The classical books Matsumura - "Commutative ring theory" and Atiyah-Macdonald - "Commutative algebra" are self contained (with some errors) and a good start. You will find lists of errata online.

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