Torsion sheaf

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In mathematics, a torsion sheaf is a sheaf \mathcal{F} on a site for which, for every quasi-compact U, the space of sections \Gamma(U, \mathcal{F}) is a torsion group. Similarly, for a prime number l, we say a sheaf \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]


  1. ^ Milne 2012, Remark 17.6