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

Milne 2012, Remark 17.6

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References

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

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[1] Milne 2012, Remark 17.6