Algebraic Groups and Representations

Workshop: Structure of algebraic groups

June 16, 2014 to June 20, 2014

A series of talks given by the participants shall discuss the theme of rational points on equivariant compactifications of algebraic groups, in particular Gabber's recent construction of compactifications of algebraic groups over arbitrary fields with positive characteristic, generalizing the wonderful compactification in the semisimple case. This uses the structure theory of pseudo-reductive groups that is discussed in week 2.

Planned schedule

Monday 16

9:00-10:00 - Introduction (Brian Conrad)

10:30-11:30 - The affine case over a perfect field (Nivedita Bhaskhar)

12:00-13:00 - Compactifications of tori (Ting-Yu Lee)

Tuesday 17

9:00-10:30 - The wonderful compactification of a semisimple adjoint group, I (Jacopo Gandini)

11:00-12:30 - The wonderful compactification of a semisimple adjoint group, II (Alexis Tchoudjem)

Wednesday 18

9:00-10:00 - Pseudo-complete varieties (Laurent Moret-Bailly)

10:30-11:30 - Group extensions controlling splitness (Philippe Gille)

12:00-13:00 - Dévissage, I (Yong Hu)

Thursday 19

9:00-10:00 - Dévissage, II (Yong Hu)

10:30-11:30 - Compactification of unipotent groups (Ziyang Gao)

12:00-13:00 - Weil restriction and Hilbert schemes (Laurent Moret-Bailly)

Friday 20

9:00-10:00 - The standard pseudo-reductive case (Philippe Gille)

10:30-11:30 - Examples of compactifications of exotic pseudo-reductive groups (Brian Conrad)

12:00-13:00 - Conclusions (Brian Conrad)

Bibliography

Section 8 of Borel-Tits, Groupes réductifs, Publ. Math. IHES 27 (1965), 55-150.

Section 10.2 of Bosch, Lütkebohmert, Raynaud, Néron Models, Ergebnisse der Mathematik und ihrer Grenzgebiete 21 (1990), Springer.

Chapter 6.1 in Brion-Kumar, Frobenius Splitting Methods in Geometry and Representation Theory, Progress in Mathematics 231 (2005), Birkäuser.

Appendices of Conrad-Gabber-Prasad, Pseudo-reductive groups, Cambridge University Press (2010).

A. Grothendieck, Techniques de construction et théorèmes d'existence en géométrie algébrique IV : les schémas de Hilbert. Séminaire Bourbaki, 6 (1960-1961), Exposé No. 221, 28.

N. Nitsure, Construction of Hilbert and Quot schemes, Fundamental Algebraic Geometry: Grothendieck's FGA explained, AMS "Math. Surveys Monogr." 123, 2005 ; p. 105-137.

Participants

Main scientific organizer: Brian Conrad (Stanford)

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