In
mathematics
Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...
, a torsion sheaf is a
sheaf
Sheaf may refer to:
* Sheaf (agriculture), a bundle of harvested cereal stems
* Sheaf (mathematics)
In mathematics, a sheaf (: sheaves) is a tool for systematically tracking data (such as sets, abelian groups, rings) attached to the open s ...
of abelian groups
on a
site
Site most often refers to:
* Archaeological site
* Campsite, a place used for overnight stay in an outdoor area
* Construction site
* Location, a point or an area on the Earth's surface or elsewhere
* Website, a set of related web pages, typical ...
for which, for every object ''U'', the space of sections
is a
torsion abelian group In abstract algebra, a torsion abelian group is an abelian group in which every element has finite order.Dummit, David; Foote, Richard. ''Abstract Algebra'', , pp. 369 For example, the torsion subgroup of an abelian group is a torsion abelian grou ...
. Similarly, for a
prime number
A prime number (or a prime) is a natural number greater than 1 that is not a Product (mathematics), product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime ...
''p'', we say a sheaf
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 In mathematics, a twisted sheaf is a variant of a coherent sheaf. Precisely, it is specified by: an open covering in the étale topology ''U'i'', coherent sheaves ''F'i'' over ''U'i'', a Čech 2-cocycle ''θ'' for \mathbb_m on the coverin ...
Notes
References
*
* J. S. Milne, ''Étale Cohomology''
*
Sheaf theory
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