2013
DOI: 10.1007/978-93-86279-58-3
|View full text |Cite
|
Sign up to set email alerts
|

Lectures on the structure of algebraic groups and geometric applications

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
1
1
1
1

Citation Types

1
47
0

Year Published

2013
2013
2024
2024

Publication Types

Select...
5
2

Relationship

3
4

Authors

Journals

citations
Cited by 53 publications
(48 citation statements)
references
References 40 publications
1
47
0
Order By: Relevance
“…This result is proved in Section 2, first in the case where char(k) = 0; then we adapt the arguments to the case of prime characteristics, which is technically more involved due to group schemes issues. We rely on fundamental results about the structure and actions of algebraic groups over an algebraically closed field, for which we refer to the recent exposition [4].…”
Section: Introduction and Statement Of The Resultsmentioning
confidence: 99%
See 2 more Smart Citations
“…This result is proved in Section 2, first in the case where char(k) = 0; then we adapt the arguments to the case of prime characteristics, which is technically more involved due to group schemes issues. We rely on fundamental results about the structure and actions of algebraic groups over an algebraically closed field, for which we refer to the recent exposition [4].…”
Section: Introduction and Statement Of The Resultsmentioning
confidence: 99%
“…Thus, π * (O X ) = O Y ×Y by Zariski's Main Theorem. It follows that π induces a homomorphism of algebraic groups [4,Cor. 4.2.6]).…”
Section: ⊓ ⊔mentioning
confidence: 97%
See 1 more Smart Citation
“…To state it, we need to introduce some notation. Recall that by Chevalley's theorem G is an extension of an abelian variety A by a linear algebraic group G aff (see [4], [5], [6], [22]). Denote by g the dimension of A and by r the rank of G aff (which is by definition the dimension of a maximal torus).…”
Section: Introductionmentioning
confidence: 99%
“…Note that if f : X −→ Y is a proper morphism between algebraic varieties such that φ * (O X ) = O Y , and if G acts on X, by a result of Blanchard (see also [BSU13, Prop. 4.2.1]), then there exists a unique action of G on Y such that f is G-equivariant.…”
Section: G-equivariant Morphisms Between G/h-embeddingsmentioning
confidence: 99%