Torsion sheaf

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.^[1]

See also[]

• Twisted sheaf

Notes[]

References[]

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

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