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

gollark: I think it must be somehow autoupdating to an older version somehow.

gollark: PotatOS just downloaded stuff into neat `/bin`, `/lib` and `/dat` folders... then decided to download stuff to a random place?

gollark: Okay, wow, that went weirdly.

gollark: Well, strictly speaking I probably *should* do that.

gollark: Oh, right, a _ENV/_G mismatch issue again...

References

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

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[1] Milne 2012, Remark 17.6