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From Higher Invariants

AG-Seminar (Kerz) SS 2017

Date and location

Monday, 16:15 - 17:45 in BIO 1.1.34

Program

The goal of the first part of the seminar (from 24.4 to 29.5) is to give an introduction on some of the known results on the Chow groups of 0-cycles on a singular variety, a theory that has been an active area of research starting from the 1980’s, and to survey some old and new results.

The program is available here: Cycles on Singular varieties, together with an extensive list of references.

In the second part of the seminar (from 5.6 until the end of the term) we will give an overview of Deligne’s proof of the Weil conjecture. The main source that we will follow is the online version of Milne’s book on étale cohomology (Lectures on étale cohomology). Other references are Jannsen’s lecture notes (available online) or the book by Freitag and Kiehl. This seminar is organised as a reading course. We will assume some basic results from algebraic geometry and some facts about étale cohomology. We will not give a complete proof of the conjectures; in particular, the so-called “Main Lemma” will be used as a black box.

The program for the second part is available here: Weil conjectures

Date Speaker Topic
24.04. Discussion General introduction and distribution of the talks
1.5. - No seminar
8.5. Morten Lüders Definitions and examples
15.5 Yigeng Zhao The case of surfaces
22.5 Enlin Yang The Bloch-Srinivas conjecture
29.5 Johann Haas Albanese and Picard varieties in the singular case
--- --- ---
12.6. Gesina Schwalbe Poincaré duality and Lefschetz fixed point formula
19.6. - No seminar
28.6. 14:15 Massimo Pippi Talk on master thesis
03.7. Massimo Pippi (?) Cohomology of Lefschetz pencils - 1
10.7. Massimo Pippi (?) Cohomology of Lefschetz pencils - 2
17.7. Yassin Mousa End of the proof
24.7. Andreas Pangerl Talk on master thesis