18.917. Algebraic K-theory. Spring 2012.
Announcements.
- Welcome! In this course, we will study the algebraic K-theory of higher categories, with the aim (time permitting) of proving a dévissage conjecture of Thomason. Here is a broad outline.
Basic information.
- Lecture times: Tuesday and Thursday, 1-2:30.
- Lecture location: 2-255
Calendar.
- Week #17 Feb. Euler characteristics and K-theory. PDF.
9 Feb. Waldhausen categories, and a delooping of the universal property of the K. PDF. - Week #214 Feb. From relative categories to quasicategories. PDF.
16 Feb. Fibrations. PDF. - Week #321 Feb. MIT Monday.
23 Feb. Limits and colimits in ∞-categories PDF. - Week #428 Feb. Pairs of ∞-categories and Waldhausen ∞-categories PDF.
1 Mar. Virtual Waldhausen ∞-categories I PDF. - Week #56 Mar. Virtual Waldhausen ∞-categories II.
8 Mar. Filtered objects PDF. - Week #613 Mar. Distributive virtual Waldhausen ∞-categories PDF.
15 Mar. Additive theories PDF. - Week #720 Mar. Goodwillie additivization PDF.
22 Mar. Excision and Waldhausen's fibration theorem PDF. - Week #827 Mar. Spring break.
29 Mar. Spring break. - Week #93 Apr. Labeled Waldhausen ∞-categories PDF.
5 Apr. Localization PDF. - Week #1010 Apr. K-theories of schemes and stacks I.
12 Apr. K-theories of schemes and stacks II. - Week #1117 Apr. Patriot's Day; no classes.
19 Apr. Exact ∞-categories PDF. - Week #1224 Apr. Overview on the Q construction.
26 Apr. A weak dévissage theorem. - Week #131 May. K-theory and the Q construction.
3 May. Interlude: Nonconnective deloopings of K-theory. - Week #148 May. t-structures and K-theory PDF.
10 May. . - Week #1515 May. No lecture.
17 May. No lecture.