Fixed Point Formula of Lefschetz Type in Arakelov Geometry I: Statement and Proof

摘要

The authors consider arithmetic varieties endowed with an action of the group211u001escheme of n-th roots of unity and they define equivariant arithmetic K0-theory 211u001efor these varieties. They use the equivariant analytic torsion to define direct 211u001eimage maps in this context and prove a Riemann-Roch theorem for the natural 211u001etransformation of equivariant arithmetic K0-theory induced by the restriction to 211u001ethe fixed point scheme; this theorem can be viewed as an analog, in the context 211u001eof Arkelov geometry, of the regular case of the theorem proved by P. Baum, W. 211u001eFulton, and G. Quart in (BaFQ).