Prof. Dr. Michael Rapoport (SS 2008)

Vorlesung (V5A2 Advanced Algebra II)
Moduli of elliptic curves

(Di 10 - 12, Do 14 - 16, SR A)

The subject matter of the course are the moduli spaces of elliptic curves with level structure, their compactification and their reduction modulo p. The study of these moduli spaces will on the one hand be a good occasion to study the abstract scheme-theoretic methods of Grothendieck in a concrete situation; on the other hand, the moduli spaces of elliptic curves are a special case of moduli spaces of abelian varieties, a still largely unknown territory and a topic of current research. Therefore the course is intended at the same time as an occasion to solidify one's aquaintance with the theory of schemes and as an introduction to a hot topic.

Prerequisites: Algebraic geometry 1 - 2.

Literature: Deligne, P.; Rapoport, M., Les schémas de modules de courbes elliptiques. (French) Modular functions of one variable, II (Proc. Internat. Summer School, Univ. Antwerp, Antwerp, 1972), pp. 143--316. Lecture Notes in Math., Vol. 349, Springer, Berlin, 1973.

Katz, N.; Mazur, B. Arithmetic moduli of elliptic curves. Annals of Mathematics Studies, 108. Princeton University Press, Princeton, NJ, 1985. xiv+514 pp.

Conrad, B., Arithmetic moduli of generalized elliptic curves. J. Inst. Math. Jussieu 6 (2007), no. 2, 209--278.

Conrad, B., Minimal models for elliptic curves.

Letzte Ă„nderung: 15.03.2010, Sekretariat Prof. Dr. M. Rapoport