Actions of $μ_p$ on canonically polarized surfaces in characteristic p>0

This paper studies the existence of non trivial $μ_p$ actions on a canonically polarized surface X defined over an algebraically closed field of characteristic p>0. In particular, an explicit function $f(K_X^2)$ is obtained such that if $p>f(K_X^2)$, then there does not exist a non trivial $μ_p$-action on X. This implies that the connected component of the automorphism scheme of X containing the identity is either smooth or is obtained by successive extensions by $α_p$.

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