Chennai Mathematical Institute

Seminars




Lecture Series Announcement
Date: 5, 9, 11, 16, 18, 19, 22, 23, 24, 25 January 2024
Time: 3:30 PM
Venue: Seminar Hall. The lectures will be given in hybrid mode.
Lectures on SGA3

Patrick Polo
Institut de Mathématiques, Université Pierre et Marie Curie, Paris.
24-01-24


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.

See the course website for more details:
https://www.cmi.ac.in/activities/kohli-centre/patrick-polo-2023/