Torsion sheaf

In mathematics, a torsion sheaf is a sheaf of abelian groups $$\mathcal{F}$$ on a site for which, for every object U, the space of sections $$\Gamma(U, \mathcal{F})$$ is a torsion abelian group. Similarly, for a prime number p, we say a sheaf $$\mathcal{F}$$ 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.