The commutative algebraic groups over a prescribed field k form an abelian category Ck; the finite commutative algebraic groups form a full subcategory Fk, stable under taking subobjects, quotients and extensions. This mini-course will study the categories Ck and Ck/Fk (the isogeny category) from a homological viewpoint, emphasizing the analogies and differences with categories of representations. In particular, we will show that Ck/Fk has homological dimension 1, and we will describe the projective and the injective objects in Ck and Ck/Fk.
These videos were produced by Syracuse University Department of Mathematics as part of ICRA 2016.
