scholarly journals On the essential dimension of unipotent algebraic groups

2013 ◽  
Vol 217 (3) ◽  
pp. 432-448 ◽  
Author(s):  
Nguyê˜n Duy Tân
Keyword(s):  
Algebraic Groups ◽  
Essential Dimension ◽  
Unipotent Algebraic Groups

Galois Cohomology of Unipotent Algebraic Groups and Field Extensions

2011 ◽  
Vol 39 (11) ◽  
pp. 3923-3938 ◽  
Author(s):  
Nguyêñ Duy Tân ◽  
Nguyêñ Quôć Thǎńg
Keyword(s):  
Algebraic Groups ◽  
Galois Cohomology ◽  
Field Extensions ◽  
Unipotent Algebraic Groups

scholarly journals Waring’s problem for unipotent algebraic groups

2019 ◽  
Vol 69 (4) ◽  
pp. 1857-1877 ◽  
Author(s):  
Michael Larsen ◽  
Dong Quan Ngoc Nguyen
Keyword(s):  
Algebraic Groups ◽  
Waring’S Problem ◽  
Waring's Problem ◽  
Unipotent Algebraic Groups

scholarly journals A fiber dimension theorem for essential and canonical dimension

2012 ◽  
Vol 149 (1) ◽  
pp. 148-174 ◽  
Author(s):  
Roland Lötscher
Keyword(s):  
Algebraic Geometry ◽  
Lower Bound ◽  
Finite Type ◽  
Algebraic Groups ◽  
General Version ◽  
Essential Dimension ◽  
Algebraic Stacks ◽  
Algebraic Tori ◽  
Canonical Dimension

AbstractThe well-known fiber dimension theorem in algebraic geometry says that for every morphism f:X→Y of integral schemes of finite type the dimension of every fiber of f is at least dim X−dim Y. This has recently been generalized by Brosnan, Reichstein and Vistoli to certain morphisms of algebraic stacks f:𝒳→𝒴, where the usual dimension is replaced by essential dimension. We will prove a general version for morphisms of categories fibered in groupoids. Moreover, we will prove a variant of this theorem, where essential dimension and canonical dimension are linked. These results let us relate essential dimension to canonical dimension of algebraic groups. In particular, using the recent computation of the essential dimension of algebraic tori by MacDonald, Meyer, Reichstein and the author, we establish a lower bound on the canonical dimension of algebraic tori.

Unipotent Algebraic Groups

1974 ◽  
Author(s):  
Tatsuji Kambayashi ◽  
Masayoshi Miyanishi ◽  
Mitsuhiro Takeuchi
Keyword(s):  
Algebraic Groups ◽  
Unipotent Algebraic Groups
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