Torsion sheaf

In mathematics, a torsion sheaf is a sheaf $\mathcal{F}$ on a site for which, for every quasi-compact U, the space of sections $\Gamma(U, \mathcal{F})$ is a torsion group. Similarly, for a prime number l, we say a sheaf $\mathcal{F}$ is l-torsion if every section over any quasi-compact is killed by a power of l.

A torsion sheaf on an étale site is the union of its constructible subsheaves.^[1]

Notes

1. ↑ Milne 2012, Remark 17.6

References

• J. S. Milne (2012). "Lectures on Étale Cohomology
• J. S. Milne, Étale Cohomology