nLab constructible sheaf

Idea

A sheaf on an étale site is constructible if its restriction to a suitable decomposition into constructible subsets is a locally constant sheaf.

References

Original articles include

• Pierre Deligne, La conjecture de Weil. II. Inst. Hautes ´Etudes Sci. Publ. Math., (52):137–252, 1980.

• Torsten Ekedahl, On the adic formalism. In The Grothendieck Festschrift, Vol. II, volume 87 of Progr. Math., pages 197–218. Birkhäuser Boston, Boston, MA, 1990.

• Alexander Beilinson, Constructible sheaves are holonomic, Selecta Mathematica 22 (2016) 1797-1819; a slightly updated version (with respect to the published one) is at arxiv/1505.06768

An introductory survey is in

• Florian Klein, Gerrit Begher, Constructible Sheaves and their derived category (pdf)

A list of relevant definitions and facts is at

• Günter Tamme, section II 9.3.2 Introduction to Étale Cohomology

• James Milne, section 17 Lectures on Étale Cohomology

• The Stacks Project, 44.62. Constructible sheaves

and with more on chain complexes of sheaves and abelian sheaf cohomology in

• Bhargav Bhatt, Peter Scholze, section 6.3 of The pro-étale topology for schemes (arXiv:1309.1198)

with an eye towards the application in l-adic cohomology/the pro-étale topos.

See also

• Jacob Lurie, Constructible sheaves (pdf)