Pseudo-reductive Groups

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Rational Points on Varieties (2017, background): “For instance, if G is a connected affine algebraic group, the unipotent radical of Gk need not descend to an algebraic group over k: see [CGP08] for details.”
Affine representability results in 1–homotopy theory, II : Principal bundles and homogeneous spaces (2015, unknown): “Acknowledgements The authors would like to thank Brian Conrad for extremely helpful correspondence regarding [22; 23].”
Some structure theorems for algebraic groups (2015, methodology): “It is based on Weil restriction; we refer to Appendix A of [20] for the definition and main properties of this notion.”
Weil and Grothendieck approaches to adelic points (2012, background): “Moreover, (i) some references that discuss the matter in the non-affine case have errors in the description of the topology on adelic points, and (ii) much of what we prove is needed in my paper [Con], or in arithmetic arguments in [CGP].”