Prerequisites in Algebraic Topology:

The students should be familiar with fundamental group, singular homology, cellular homology, CW-complexes and basic computations. The axiomatic approach.

References:

A. Hatcher, Algebraic topology, Cambridge Univ. Press, Available online here.
J.R. Munkres, Elements of Algebraic Topology, Menlo Park Addison-Wesley.
C. A. Weibel, An introduction to homological algebra, Cambridge Univ. Press. 1994.
More advanced: J. P. May, A Concise Course in Algebraic Topology

Prerequisites in Algebraic Geometry:

First properties of schemes and morphisms (separeted, proper, projective, smooth, flat). Basics on formal schemes and group schemes.

References:

Qing Liu, Algebraic Geometry and Arithmetic Curves, Oxford University Press, 2002
R. Hartshorne, Algebraic Geometry, Springer-Verlag, 1977
D. Mumford, Red Book of Varieties and Schemes, Springer-Verlag, ed. 1999
D. Mumford, Abelian Varieties, Oxford University Press, 1970