Algebraic structures

The goal of this course is to introduce and study the basic notions of abstract algebra.

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Rings and fields

This is an introductory course to the theory of rings and fields.

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Rings and modules

The students are going to solidify their knowledge of ring and module theory with a major emphasis on commutative algebra and a minor emphasis on homological algebra.

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Modern algebraic geometry

The aim of this course is to learn the basics of the modern scheme theoretic language of algebraic geometry.

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Group schemes

This is a course about group schemes, with an emphasis on structural theorems for algebraic groups (e.g. Barsotti--Chevalley's theorem). All the basics will be covered towards the proof of such theorem, with an estress on the modern presentation using scheme theory and modern algebraic geometry.

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