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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：On open subgroups of p-adic algebraic groups
p-adic 代数群 开子群
2023/5/5
In this talk, I will breifly introduce the p-aidc number, p-aidc manifolds, p-adic algebraic groups and p-aidc definable groups. Using an elementary method, I will show that every open subgroup of a c...
This paper is the sequel to The radiance obstruction and par-
allel forms on a;ffne manifolds (lYans. Amer. Math. Soc. 286 (1984),
629 649) which introduced a new family of secondary characteristi...
Let k be a eld, and let G be an algebraic group over k, by which we mean a connected smooth k-group
scheme (not necessarily ane). Recall that such a G is automatically separated, nite type, and ge...
We prove the niteness of class numbers and Tate-Shafarevich sets for all ane group
schemes of nite type over global function elds, as well as the niteness of Tamagawa
numbers and Godement's com...
On the essential dimension of unipotent algebraic groups
essential dimension unipotent algebraic groups
2011/1/21
We give an upper bound for the essential dimension of a smooth unipotent algebraic group over an arbitrary field. We also show that over a field k which is finitely generated over a perfect field, a s...
Extended weight semigroups of affine spherical homogeneous spaces of non-simple semisimple algebraic groups
Extended weight semigroups affine spherical homogeneous spaces of non-simple semisimple algebraic groups
2011/1/17
The extended weight semigroup of a homogeneous space G/H of a connected semisimple algebraic group G characterizes the spectra of the repre-sentations of G on the spaces of regular sections of homogen...
G-complete reducibility and the exceptional algebraic groups
G-complete reducibility the exceptional algebraic groups
2010/11/24
Let $G=G(K)$ be a simple algebraic group defined over an algebraically closed field $K$ of characteristic $p>0$. A subgroup $X$ of $G$ is said to be $G$-completely reducible if, whenever it is contai...
Restriction maps on 1-cohomology of (algebraic) groups
Restriction maps on 1-cohomology of groups
2010/11/11
Our first theorem is a version of the five lemma in a certain situation of pointed sets arising from non-abelian 1-cohomology. For our second, we show that a connected, unipotent algebraic group Q ac...
Ultraproducts of Tannakian Categories and Generic Representation Theory of Unipotent Algebraic Groups
Ultraproducts of Tannakian Categories Representation Theory Unipotent Algebraic Groups
2010/11/9
The principle of tannakian duality states that any neutral tannakian category is tensorially equivalent to the category Rep_k G of finite dimensional representations of some affine group scheme G and ...
A Topological Version of the Borel-Tits Theorem on Abstract Homomorphisms of Simple Algebraic Groups
Topological Version Borel-Tits Theorem Simple Algebraic Groups
2010/12/9
In this paper, we produce topologized versions of two theorems. One is due to Borel and Tits [2] and is concerned with abstract homomorphisms of absolutely almost simple algebraic groups.