Derived Algebraic Geometry
General information
Outline
1. Introduction (4月9日)2025DAG01.pdfWe use Bezout's Theorem to argue that moving from sets to homotopy types is a natural progression, analogous to fields ⇝ algebraically closed fields; affine varieties ⇝ projective varieties; varities ⇝ schemes. --- 4月16日 No lecture 講義がありません ---(April 14-18 Workshop Arithmetic France-Japan - 日本 x フランス 数論幾何学 2025)2. Homotopy types (4月23日)2025DAG02.pdfWe present two models for the theory of homotopy types: simplicial sets (or rather Kan complexes) and topological spaces (or rather CW complexes). Most importantly, we define what is a space and a equivalence. --- 4月30日 No lecture 講義がありません ---3. Infinity categories (5月7日)2023DAG05.pdfWe present two models for the theory of infinity categories: quasi-categories and simplicial categories. We define the quasi-categories of spaces. 4. Limits and colimits (5月14日)2025DAG04.pdfWe discuss weighted limits in simplicial categories, and limits in quasi-categories. We relate these to each other, at least in the case of the simplicial/quasi- category of Kan complexes, that is, the ∞-category of homotopy types. 5. Topos theory (5月21日)2025DAG05.pdfNotes on the [HTT] proof of sheafification Topologies vs. pretopologies We discuss the notion of sheaf in the classical and higher settings. 6. Commutative algebra (5月28日)7.Linear algebra (6月4日)8. Deformation theory I: the cotangent complex (6月11日)9. Schemes (6月18日)10. Deformation theory II: the global cotangent complex (6月25日)--- 7月2日 No lecture 講義がありません ------ 7月9日 No lecture 講義がありません ---11. Algebraic K-theory (7月16日) |