Torsion sheaf

In mathematics, a torsion sheaf is a sheaf ${\displaystyle {\mathcal {F}}}$ on a site for which, for every quasi-compact U, the space of sections ${\displaystyle \Gamma (U,{\mathcal {F}})}$ is a torsion group. Similarly, for a prime number l, we say a sheaf ${\displaystyle {\mathcal {F}}}$ 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 harvnb error: no target: CITEREFMilne2012 (help)

References

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