---

Master Course 'Moduli of Abelian Varieties'
(MRI Master Class Spring 2011)

---

The course is about the moduli space of abelian varieties. We will concentrate on the moduli space
of principally polarized abelian varieties. The simplest example is the moduli space of elliptic curves.
This moduli space has many facets, geometric, algebraic and arithmetic and we will try to touch upon
the various aspects. Among the topics we intend to treat are compactifications,cycle classes,
cohomology and modular forms.

---

Literature will be given during the course.

---

Place and time
Wednesdays 13:00-15:00, starting Feb. 2, Room 611 of the Wiskundegebouw of the University of Utrecht.

---

A list of topics: 1) elliptic curve, abelian variety, group scheme 2) Weierstrass equation, j-invariant, complex elliptic curves, H\SL(2,Z), congruence subgroups, universal family 3) moduli of complex abelian varieties, Lefschetz theorem 4) compactification of Gamma\H for Gamma in SL(2,Z) 5) twists of elliptic curves 6) some universal families, moduli problems, coarse and fine moduli space 7) existence of the moduli space of elliptic curves 8) dual abelian variety 9) a fundamental domain for the action of Sp(2g,Z) in H_g 10) the Satake compactification 11) elliptic modular forms 12) Siegel modular forms 13) a smooth compactification