Teacher: Baptiste Morin
Program:
We will study classical topics in homological algebra, such as the theory of
abelian categories, derived functors and spectral sequences. The general theory
will be applied to define and study group chomology and/or sheaf cohomology.
If time permits we will also introduce and use the derived category of an abelian
category.
Prerequisites:
Basic concepts of category theory, general topology and commutative algebra.
References:
[1] Brown, K.S.: Cohomology of groups. Graduate Texts in Mathematics, 87. Springer-Verlag,
New York-Berlin, 1982.
[2] Cartan, H.; Eilenberg, S.: Homological algebra. Princeton University Press, Princeton, N.
J., 1956.
[3] Godement, R.: Topologie algébrique et théorie des faisceaux. Actualités Sci. Ind. No. 1252.
Publ. Math. Univ. Strasbourg. No. 13 Hermann, Paris 1958.
[4] Grothendieck, A.: Sur quelques points d’algèbre homologique. Tohoku Math. J. (2) 9 (1957),
119–221.
[5] Serre, J.P. Corps locaux. Deuxième édition. Publications de l’Université de Nancago, No.
VIII. Hermann, Paris, 1968.
[6] Weibel, C. A.: An introduction to homological algebra. Cambridge Studies in Advanced
Mathematics, 38. Cambridge University Press, Cambridge, 1994.