Torsion sheaf

In mathematics, a torsion sheaf is a sheaf of abelian groups ${\displaystyle {\mathcal {F}}}$ on a site for which, for every object U, the space of sections ${\displaystyle \Gamma (U,{\mathcal {F}})}$ is a torsion abelian group. Similarly, for a prime number p, we say a sheaf ${\displaystyle {\mathcal {F}}}$ 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.^[1]

See also

• Twisted sheaf