## Winter 2012/13

**Seminar on Motives**

- Prerequisites: Algebraic Geometry and Homological Algebra
- Detailed program: [download as PDF, version 2013-01-07]
- Time and Location: Thursday, 14-16h in SR 414
- Schedule:
- 0 - Overview (Konrad) 25.10.2012
- no seminar (Feiertag) 1.11.2012
- 1 - Tensor Cats (Oliver) 8.11.2012
- 2 - Equivalences on Cycles (Clemens) 15.11.2012
- 3 - Weil Cohomologies (Max) 22.11.2012
- 4 - Pure Motives (Konrad) 29.11.2012
- no seminar in December 2012
- 5 - Examples (Sarah) 10.1.2013
- 7 - Mixed Hodge Structures (Jan) 17.1.2013
- 6 - Standard and Weil Conjectures (Konrad) 24.1.2013
- no seminar on 31.1.2013
- 8 - Topoi (Helene) 7.2.2013
- 9 - Voevodsky's Motives (Konrad) tba in 2013

- Abstract: In this seminar we want to introduce the motivation, basic ideas and formal definitions of pure motives, using some of the prerequisites as black boxes (most notable the inner workings of intersection theory). The goal is threefold: We want to learn tools that are useful elsewhere in algebraic geometry, we want to learn the "motivic" intuition and we want to be able to read the expository literature on the subject afterwards. We will also try to get an idea of mixed motives, using as specific example Hodge theory, which some participants might be more familiar with. Our guiding examples will be elliptic curves, smooth projective curves and arbitrary curves on one side and projective space and Grassmannians on the other side.