Equivariant motivic integration on formal schemes and the motivic zeta function

摘要

For a formal scheme over a complete discrete valuation ring with a goodaction of a finite group, we define equivariant motivic integration, and weprove a change of variable formula for that.To do so, we construct and examinean induced group action on the Greenberg scheme of such a formal scheme. Usingthis equivariant motivic integration, we define an equivariant volumePoincar'e series, from which we deduce Denef and Loeser's motivic zetafunction including the action of the profinite group of roots of unity.