Goal
A linear algebraic group is an affine variety endowed with the structure of an algebraic group (such that the multiplication map and the formation of the inverse are defined by morphisms in this category. In this seminar the algebraic groups are usually supposed to be defined over an algebraically closed field k, but we will also pay attention to the case where things are defined over a subfield F of k that is not algebraically closed (they are then considered to have an additional structure).
A prime example of a linear algebraic group is GL(n,k), and indeed, we shall see that any linear algebraic group over k turns out to be isomorphic to a (Zariski) closed subgroup of some GL(n,k)).
We shall mostly follow:
T.A. Springer: Linear Algebraic Groups, Modern Birkhauser Classics (reprint of the 1998 edition)
The following two books of the same title are also useful:
A. Borel: Linear Algebraic Groups, Graduate Texts in Mathematics 126, Springer-Verlag (1991).
J.E. Humphreys: Linear Algebraic Groups, Graduate Texts in Mathematics, 21. Springer-Verlag (1975).
and so is the PDF file of the book freely available online by J. Milne: Algebraic Groups. The latter uses consistently the language of schemes (rather than of varieties), which leads to a somewhat different approach and emphasis.
Time and Place
Mondays 18:30-20:30, except on public holidays in Lecture Room 1 (1st floor) of the Jin Chun Yuan West Building,
Program and covered material
Sept. 13: Yiming Zhong: Ch. 1 (review of algebraic geometry).
Sept. 20: Bingyi Chen: Ch. 2, sections 1,2,3.
Sept. 27: Yunpeng Zi: Ch. 2, sections 3,4,5.
Oct. 10: Peigen Li: Ch. 3, sections 1,2.
Oct. 17: Peigen Li: Ch. 3, until 3.4.7.
Oct. 24: Peigen Li: finished Ch. 3, Zhung Xuchang: Ch. 4 until 4.2.6.
Oct. 31: Zhiwei Zheng: 4.3, 4.4.
Nov. 7: Yiming Zhong: 5.1, 5.2.
Nov. 14: Yiming Zhong: 4.3, 4.4.
Nov. 21: Bin Wang: 5.3, 5.4.
Nov. 28: Bin Wang: 5.6, Xiaoyu Su: 6.1.
Dec. 5: Xiaoyu Su: until halfway 6.3.
Dec. 12: Xiaoyu Su: Ch. 6 (Cartan subgroups).
Dec. 19: Xiaoyu Su finished Ch. 6.
Dec. 26: Zhengping Gui: finished almost the first two sections of Ch. 7.
Next meeting: Jan. 5 2017 (Thursday!): Zhengping Gui will finish Ch. 7; Yinbang Lin will continue with Ch. 8.
Contact and in charge of the organization: 王彬