Finite generation conjectures for cohomology over finite fields
  We construct an intermediate cohmology between motivic cohomology and Weil-etale cohomology. Using this, the Bass conjecture on finite generation of motivic cohomology, and the Beilinson-Tate on the finite generation of Weil-etale cohomology are related. 
Thomas H Geisser
math.KT math.NT