# Pseudo-reductive Groups

@inproceedings{Conrad2010PseudoreductiveG, title={Pseudo-reductive Groups}, author={Brian Conrad and Ofer Gabber and Gopal Prasad}, year={2010} }

Preface to the second edition Introduction Terminology, conventions, and notation Part I. Constructions, Examples, and Structure Theory: 1. Overview of pseudo-reductivity 2. Root groups and root systems 3. Basic structure theory Part II. Standard Presentations and Their Applications: 4. Variation of (G', k'/k, T', C) 5. Ubiquity of the standard construction 6. Classification results Part III. General Classification and Applications: 7. The exotic constructions 8. Preparations for classification…

## 289 Citations

### On Unipotent Radicals of Pseudo-Reductive Groups

- MathematicsMichigan Mathematical Journal
- 2019

We establish some results on the structure of the geometric unipotent radicals of pseudo-reductive k-groups. In particular, let k' be a purely inseparable field extension of k of degree p^e and let G…

### Reductive Group Schemes (sga3 Summer School, 2011)

- Mathematics
- 2011

The aim of these notes is to develop the theory of reductive group schemes, incorporating some simplifications into the methods of [SGA3]. We assume the reader is familiar with the basic structure…

### REDUCTIVE GROUPS OVER FIELDS LECTURES BY BRIAN CONRAD, NOTES BY TONY FENG

- Mathematics
- 2016

1. Basic structure of reductive groups 2 2. The unipotent radicals 9 3. Central isogeny decomposition 14 4. Grothendieck’s covering theorem 24 5. Exponentiating root spaces 29 6. Dynamic description…

### Linear algebraic groups with good reduction

- Mathematics
- 2020

This article is a survey of conjectures and results on reductive algebraic groups having good reduction at a suitable set of discrete valuations of the base field. Until recently, this subject has…

### Linear algebraic groups with good reduction

- MathematicsResearch in the Mathematical Sciences
- 2020

This article is a survey of conjectures and results on reductive algebraic groups having good reduction at a suitable set of discrete valuations of the base field. Until recently, this subject has…

### Pseudo-reductive and quasi-reductive groups over non-archimedean local fields

- MathematicsJournal of Algebra
- 2018

### GENERICALLY FREE REPRESENTATIONS II: IRREDUCIBLE REPRESENTATIONS

- MathematicsTransformation Groups
- 2020

We determine which faithful irreducible representations V of a simple linear algebraic group G are generically free for Lie(G), i.e., which V have an open subset consisting of vectors whose…

### Generically free representations III: exceptionally bad characteristic

- Mathematics
- 2018

In parts I and II, we determined which irreducible representations $V$ of a simple linear algebraic group $G$ are generically free for Lie($G$), i.e., which $V$ have an open subset consisting of…

### Complete reducibility of subgroups of reductive algebraic groups over nonperfect fields III

- MathematicsCommunications in Algebra
- 2019

Abstract Let G be a reductive group over a nonperfect field k. We study rationality problems for Serre’s notion of complete reducibility of subgroups of G. In our previous work, we constructed…

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