Title: Coherent Functors

Abstract: Auslander introduced coherent functors on abelian categories.

I will talk about coherent functors on the category of finitely generated modules over a noetherian commutative ring.

A  covariant functor from this category to itself is coherent if it is the cokernel of a map between two homfunctors.

Examples are given by such homfunctors and the derived functors Ext and Tor.

I and my student Adson Banda proved  in this context asymptotic stability for sequences of sets of prime ideals connected with powers of an ideal generalising results by me and Peter Schenzel.

I will also say something about coherent functors on other abelian categories.