Invariants, cohomologie et représentations fonctorielles des groupes algébriques images
Invariants, cohomologie et représentations fonctorielles des groupes algébriques
Book in French — English title: Invariants, Cohomology and Functorial Representations of Algebraic Groups
The material presented in this book is a detailed version of a Cours Peccot given in the spring of 2010 at the Collège de France.
The course deals with invariant theory and group cohomology. It presents an approach to these two classical subjects in terms of functor categories. This functorial approach emerged in the last decade of the 20th century and has led to significant progress in both subjects.
One of the major results presented in this course is the proof of a conjecture of van der Kallen. This conjecture predicts that the finite generation properties of algebras of invariants of reductive groups (discovered by Hilbert at the end of the nineteenth century) extend to cohomology algebras. The conjecture was proved in joint work with van der Kallen, which gives pride of place to classical invariant theory and to the study of cohomology by functorial methods.
Antoine Touzé
A former student of the ENS Cachan, a Supélec engineer and agrégé in mathematics, he wrote his doctoral thesis on homological algebra in functor categories under the supervision of V. Franjou at the Université de Nantes.
In 2009 he became a senior lecturer (maître de conférences) at Université Paris 13, and in 2015 a professor at the Université de Lille.
His interests include the representation theory of algebraic groups, group homology, K-theory, and the links between these topics and functor categories.
In 2010 he was awarded the Cours Peccot at the Collège de France for his early work on these subjects.
- Reference S-092-P
- ISBN 978-2-36693-092-4
- EAN13 9782366930924
- Language French
- Pages 108
- Size 16x24
- Weight 250g
- Color Yes
@book{Touze2022,
title = {{Invariants, cohomologie et repr{\'e}sentations fonctorielles des groupes alg{\'e}briques}},
author = {Touz{\'e}, Antoine},
year = {2022},
series = {Spartacus Sup{\'e}rieur},
publisher = {Spartacus-Idh},
ISBN = {978-2-36693-092-4},
pages = {108},
url = {https://spartacus-idh.com/liseuse/092/}
}
