Brauer groups and Galois cohomology
Termine und Zeiten:
Vorlesungen: Montag, 16-18 ct, Raum B 046.
Übungen: Dienstag, 16-18 ct, Raum B 046.
Zusammenfassung:
This course follows the book by Gille and Szamuely and introduces central simple algebras and the Brauer group. We will explore their connections to Galois cohomology and Severi–Brauer varieties.
Voraussetzung:
This course will be of interest to Master students majoring in Algebra. I will assume that the students are familiar with Algebra I & II courses. Knowledge of Algebraic Geometry is not strictly required, but will be helpful. The course will be taught in English.
Exam:
The exam will take place on Tuesday 14 July from 16:15 until 17:15 in room B 046. No materials are permitted in the exam. Please ensure you bring with you an appropriate identity document with photo.
If you are considering taking the exam, please register by sending me a short email with your name, Hauptfach, and Matrikelnr.
Literatur:
[1] P. Gille and T. Szamuely, Central Simple Algebras and Galois Cohomology. Cambridge: Cambridge University Press, 2006.
[2] M.-A. Knus, A. Merkurjev, M. Rost, J.-P. Tignol, The Book of Involutions. AMS Colloquium Publications, 1998.
[3] T. Y. Lam, A First Course in Noncommutative Rings. Graduate Studies in Mathematics, 2001.
[4] T. Y. Lam, Introduction to Quadratic Forms over Fields. Graduate Studies in Mathematics, 2005.
[5] J. P. Serre, Local Fields. Graduate Texts in Mathematics, 1979.
[6] J. P. Serre, Galois Cohomology. Springer Monographs in Mathematics, 1997.