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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.

See also

• Twisted sheaf

Notes

1. Milne 2012, Remark 17.6

References

• Milne, James S. (2012). "Lectures on Étale Cohomology" (PDF).
• J. S. Milne, Étale Cohomology
• Fu, Lei (2015). Etale Cohomology Theory. Nankai Tracts in Mathematics. Vol. 14. doi:10.1142/9569. ISBN 978-981-4675-08-6.

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