Bell, Jason Pierre; Ghioca, Dragos; Tucker, Thomas John Applications of \(p\)-adic analysis for bounding periods of subvarieties under étale maps. (English) Zbl 1349.14002 Int. Math. Res. Not. 2015, No. 11, 3576-3597 (2015). Summary: Using methods of \(p\)-adic analysis, we obtain effective bounds for the length of the orbit of a preperiodic subvariety \(Y \subset X\) under the action of an étale endomorphism of \(X\). As a corollary of our result, we obtain effective bounds for the size of torsion of any semiabelian variety over a finitely generated field of characteristic 0. Our method allows us to show that any finitely generated torsion subgroup of \(\mathrm{Aut}(X)\) is finite. This yields a different proof of Burnside’s problem for automorphisms of quasiprojective varieties \(X\) defined over a field of characteristic 0. Cited in 9 Documents MSC: 14A10 Varieties and morphisms 14G20 Local ground fields in algebraic geometry 26E30 Non-Archimedean analysis PDFBibTeX XMLCite \textit{J. P. Bell} et al., Int. Math. Res. Not. 2015, No. 11, 3576--3597 (2015; Zbl 1349.14002) Full Text: DOI arXiv