Transfer Functors on k-Algebras, by Charles A. Weibel

We introduce and study the notion of a transfer functor for normal algebras over a field, i.e., a functor equipped with transfer maps for finite integral extensions. The prototypical transfer functors are: the forgetful functor F(A)=A, equipped with trace maps, and the units functor U(A)=A*, equipped with norm maps. Any Hecke functor for the absolute Galois group (such as a Galois module) induces a transfer functor, and conversely.

Our notion is a modification of Voevodsky's notion of presheaf with transfers, taking advantage of the fact that every correspondence may be normalized, and is inspired by the work of Suslin and Voevodsky.

This paper appeared in J. Pure Applied Algebra 201 (2005), 340-366.

Charles A. Weibel <>