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Very special algebraic groups
- Publication Year :
- 2020
- Publisher :
- arXiv, 2020.
-
Abstract
- We say that a smooth algebraic group $G$ over a field $k$ is very special if for any field extension $K/k$, every $G_K$-homogeneous $K$-variety has a $K$-rational point. It is known that every split solvable linear algebraic group is very special. In this note, we show that the converse holds, and discuss its relationship with the birational classification of algebraic group actions.<br />Comment: Proof of Lemma 6 simplified following a suggestion of the referee
- Subjects :
- Linear algebraic group
Pure mathematics
General Mathematics
010102 general mathematics
Field (mathematics)
Group Theory (math.GR)
01 natural sciences
Mathematics - Algebraic Geometry
Field extension
Algebraic group
14L10 (Primary) 14M17, 20G15 (Secondary)
0103 physical sciences
Converse
FOS: Mathematics
Point (geometry)
010307 mathematical physics
0101 mathematics
Algebraic number
Mathematics - Group Theory
Algebraic Geometry (math.AG)
Mathematics
Subjects
Details
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....4ae911fbc7df0223538451faa7fa8f54
- Full Text :
- https://doi.org/10.48550/arxiv.2002.06940