同济大学数学科学学院
2025-26学年第一学期
时间：TBA
地点：TBA
1. 单纯层的同伦论([MV99, First half of Section 2.1])(TBA)
2. Eilenberg-Mac Lane层与Postnikov塔([MV99, Second half of Section 2.1])(TBA)
3. 单纯层的局部对象与局部化([MV99, Section 2.2])(TBA)
4. 带区间的景的同伦范畴([MV99, Section 2.3])(TBA)
5. Nisnevich拓扑([MV99, Section 3.1])(TBA)
6. A1-同伦范畴([MV99, First half of Section 3.2])(TBA)
7. 粘合与同伦纯粹性([MV99, Second half of Section 3.2])(TBA)
8. 谱与S1-稳定同伦([BF78], [Mor05, Section 2])(TBA)
9. 悬挂，Eilenberg-Mac Lane谱和Postnikov塔([Mor05, Section 3.1, 3.2])(TBA)
10. A1局部化([Mor05, Section 4.1, 4.2])(TBA)
11. A1连通性定理([Mor05, Section 6.1])(TBA)
12. P1谱([Mor02, Section 5.1])(TBA)
13. 同伦t结构与同伦模([Mor05, Section 3.3, 6.2], [Mor02, Section 4.3, 5.2])(TBA)
14. Milnor-Witt K理论与Motivic稳定同伦群([Mor02, Section 6.3, 6.4])(TBA)
15. Grothendieck六个函子([CD19, Section 2])(TBA)
参考文献：
[Art62] M. Artin, Grothendieck topologies, Cambridge, Mass.: Harvard University. 133 p. (1962).
[BF78] Homotopy theory of Γ-spaces, spectra, and bisimplicial sets, in Geometric Applications of Homotopy Theory (Proc. Conf., Evanston, Ill., 1977), II, Lecture Notes in Math., Vol. 658, Springer, Berlin (1978), pp. 80-130.
[CD19] D.-C. Cisinski, F. Deglise, Triangulated categories of motives, Springer Monographs in Mathematics. Springer, Cham, 2019.
[Mor02] F. Morel, Introduction to A1-homotopy theory, Lectures given at the School on Algebraic K-Theory and its Applications, ICTP, Trieste. 8-19 July, 2002.
[Mor05] F. Morel, The stable A1-connectivity theorems, K-Theory 35 (2005), no.1-2, 1-68.
[MV99] F. Morel, V. Voevodsky, A1-homotopy theory of schemes, Publ. Math. IHES 90 (1999) 45-143 (2001).