On the automorphisms of surfaces of general type in positive characteristic (Q1261205)

Let \(X\) be a minimal surface of general type over an algebraically closed field of characteristic \(p>0\). The key result of the paper is that the order of any abelian subgroup \(A\) of \(\Aut(X)_{\text{red}}\) is bounded by \(D\cdot(K_ X^ 2)^ 4\) if \(\text{ord}(A)\) is prime to \(p\); here \(K_ X\) denotes the canonical sheaf of \(X\), and \(D\) is a universal constant independent of \(p\). From this result one can deduce in the same way as in characteristic zero [see \textit{A. T. Huckleberry} and \textit{M. Sauer}, Math. Z. 205, No. 2, 321-39 (1990; Zbl 0718.32022)] a polynomial bound for the order of any prime to \(p\) subgroup of \(\Aut(X)_{\text{red}}\).