April 2026
Brauer Group
An introduction to Brauer groups, first for a field (i.e., Spec k for a geometer) and then for a scheme.
AlgebraAlgebraic Geometry
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Algebra
June 2025
Representation Theory
Basics on the representation of complex semisimple Lie algebras, with some examples worked out.
Algebra
Read more →March 2025
Tilting
An introduction to the machinery of tilting sheaves for writing down derived equivalences. In particular, we compute the functors explicitly in some examples.
AlgebraCategory Theory
Read more →July 2022
Nullstellensatz
Hilbert's Nullstellensatz bridges algebra and geometry. This article develops commutative algebra before arriving at a proof.
Algebra
Read more →December 2021
Sylow Theorems
The Sylow Theorems are fundamental to finite groups. We build toward their proof through group actions, existence, and conjugation.
Algebra
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FTFGMPID
The Fundamental Theorem of Finitely Generated Modules over a PID quickly gives the classification of finitely generated abelian groups and Jordan normal form.
Algebra
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