These study notes are based on a seminar talk by Myung Jin Jeong, with notes written by Hyeongmuk Lim (May 9, 2025).
The manuscript explores the relationship between geometric spaces and their algebras of functions, and develops a path toward non-commutative geometry through homological and categorical ideas.
Contents
- Introduction: affine spaces and non-affine spaces
- First step toward non-commutative geometry, including Hochschild (co)homology
- Spectra, (co)homology theories, and stabilization
- Geometry of categories, spectral algebraic geometry, and motives
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