Automorphisms of a surface of general type acting trivially in cohomology

Abstract

It is proved that, for a complex minimal smooth projective surface $S$ of general type, any automorphism group of $S$, inducing trivial actions on the second rational cohomology of $S$, is isomorphic to a cyclic group of order less than five or the product of two groups of order two, provided that the Euler characteristic of the structure sheaf of $S$ is larger than $188$.