Torsion sheaf

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

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.