In mathematics, a torsion sheaf is a sheaf of abelian groups F {\displaystyle {\mathcal {F}}} on a site for which, for every object U, the space of sections Γ ( U , F ) {\displaystyle \Gamma (U,{\mathcal {F}})} is a torsion abelian group. Similarly, for a prime number p, we say a sheaf F {\displaystyle {\mathcal {F}}} is p-torsion if every section over any object is killed by a power of p. A torsion sheaf on an étale site is the union of its constructible subsheaves.
See also Twisted sheaf
Notes
References Milne, James S. (2012). "Lectures on Étale Cohomology" (PDF). J. S. Milne, Étale Cohomology Fu, Lei (2015). Etale Cohomology Theory. Nankai Tracts in Mathematics. Vol. 14. doi:10.1142/9569. ISBN 978-981-4675-08-6.