The number of algebraic cycles with bounded degree

 
Atsushi Moriwaki

 
 
  Let X be a projective scheme over a finite field. In this paper, we consider the asymptotic behavior of the number of effective cycles on X with bounded degree as it goes to the infinity. By this estimate, we can define a certain kind of zeta functions associated with groups of cycles. We also consider an analogue in Arakelov geometry.
 
  Comments : This is a draft version.