On the essential dimension of cyclic groups

In this paper we find an upper bound for the essential dimension ed(G) of finite cyclic groups over a field F of characteristic different from pi containing all the primitive pi-th roots of unity, where pi are distinct prime numbers. We then provide a lower bound for ed(G) in terms of the canonical dimension cdim(A) of some central division algebra A. This lower bound coincides with the upper bound thus giving the value of ed(G) if a conjecture for cdim(A) holds.