** On the Limit of Frobenius in the Grothendieck Group **

* Kazuhiko Kurano, Kosuke Ohta *

**Abstract**

Considering the Grothendieck group of finitely generated modules modulo numerical equivalence, we obtain the finitely generated lattice *R*. Let *C* _{ C M }(*R*) be the cone in *R*-modules. We shall define the fundamental class *R* in ^{ e } *R*]/*p* ^{ d e } in the case *c* *h*(*R*)=*p*>0. The homological conjectures are deeply related to the problems whether *C* _{ C M }(*R*) or the strictly nef cone *S* *N*(*R*) defined below. In this paper, we shall prove that *C* _{ C M }(*R*) in the case where *R* is FFRT or F-rational.