Brauer groups and Galois cohomology
Termine und Zeiten:
Vorlesungen: Montag, 16-18 ct, Raum B 046.Übungen: Dienstag, 16-18 ct, Raum B 046.
Please note that the lecture originally scheduled for June 29 (Monday) has been rescheduled to July 3 (Friday), and the Exercise session originally scheduled for June 30 (Tuesday) has been rescheduled to July 10 (Friday). Both the rescheduled lecture and the exercise session will take place in the usual room B 046 at the usual time 16-18 c.t.
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.
Dr. Andrei Lavrenov