Torsion sheaf

In mathematics, a torsion sheaf is a sheaf of abelian groups [math]\displaystyle{ \mathcal{F} }[/math] on a site for which, for every object U, the space of sections [math]\displaystyle{ \Gamma(U, \mathcal{F}) }[/math] is a torsion abelian group. Similarly, for a prime number p, we say a sheaf [math]\displaystyle{ \mathcal{F} }[/math] 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". https://www.jmilne.org/math/CourseNotes/LEC.pdf. 
• J. S. Milne, Étale Cohomology
• Fu, Lei (2015). Etale Cohomology Theory. Nankai Tracts in Mathematics. 14. doi:10.1142/9569. ISBN 978-981-4675-08-6.