Patrick Polo, Aug-Sep 2023 & Jan 2024Jan 2024Professor Patrick Polo from the Institut de Mathématiques, Université Pierre et Marie Curie, Paris, will be visiting CMI from January 6 till January 25, 2024. He will give a series of 7 lectures on themes from SGA 3. Title: Lectures on SGA3 Abstract: The aim of these talks is to follow up the talks from August 2023, which were centered on groups of multiplicative type and the fact that they become split after an etale extension of the base, which moreover can be taken etale and finite if the base is locally noetherian and normal. Now we plan to move forward to the case of reductive groups G. The lectures will begin with the following results, not necessarily in that order: results about Weil restriction of scalars, which imply that the centraliser and normaliser in G of a subtorus T are represented by closed, smooth subgroup schemes, the theorem of existence of maximal tori over an arbitrary field, using regular elements in the Lie algebra, and, thirdly, the existence etale-locally of maximal tori of G over an arbitrary base S. The next step will be the construction of the root subgroups, using the dynamical method of Conrad-Gabber-Prasad, and then the results of SGA3, Exposé 24 on the classification of forms of a split reductive group G over a base S in terms of Aut(G)-torsors. Lecture Schedule
Aug-Sep 2023Professor Patrick Polo from the Institut de Mathématiques, Université Pierre et Marie Curie, Paris, will be visiting CMI from August 6 till September 7, 2023. He will give a series of 8 lectures (2 per week) on themes from SGA 3. Title: Lectures on SGA3 Abstract: SGA3 was a seminar on group schemes, but it was an ideal test-ground and playground for many of the theories introduced by Grothendieck at that time: faithfully flat descent, sheaves for fpqc, fppf or étale topology, reductions to the noetherian case, infinitesimal and formal methods. All this is rather intimidating when presented in its own right. On the contrary, we intend to present a leisurely introduction, introducing concepts step by step only as needs arise for the study of reductive group schemes (and first of all, tori) and illustrating them by concrete examples. The idea is to share the joy the lecturer had by reading SGA3. Lecture Schedule
Lecture notes (These will be updated, as the lectures progress.):
Colloquium talk preprint Lecture videos |
