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I was wondering who originated the presentation of Verdier duality as an equivalence between categories of sheaves and cosheaves ? I learnt it reading Jacob Lurie's Higher Algebra and Justin Curry's article "Sheaves, cosheaves, and applications". But they don't give any references.

Certainly this is an uncommon approach for algebraic geometers. Has this been develop by topologists ? Is this part of some folklore or is there some written reference ?

Thanks.

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2 Answers 2

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Here you can read how Justin Curry describes the history, referring to early work Verdier duality on the building by Schneider, a conjecture by McPherson, and then his own 2012 paper Sheaves, Co-Sheaves, and Verdier Duality.

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    $\begingroup$ The links have rotted, maybe copy and paste the archived page's content to MO? $\endgroup$
    – Pulcinella
    Mar 7, 2023 at 0:31
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    $\begingroup$ repaired broken links, thanks for alerting me! $\endgroup$
    – Carlo Beenakker
    Mar 8, 2023 at 12:57
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Here are two references by J.L.Verdier himself :

1)J.L.Verdier(1967), "A duality theorem in the etale cohomology of schemes", Proceedings of a Conference on Local Fields: NUFFIC Summer School held at Driebergen (The Netherlands) in 1966, Springer-Verlag, pp. 184–198.

2)J.L.Verdier(1995),"Dualité dans la cohomologie des espaces localement compacts", Séminaire Bourbaki, Vol. 9, Paris: Société Mathématique de France, Exp. No.300, 337–349.

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    $\begingroup$ This doesn't answer the question asked. Verdier himself certainly didn't formulate Verdier duality as an equivalence between categories of sheaves and cosheaves. $\endgroup$
    – Dan Petersen
    Dec 18, 2014 at 14:53
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    $\begingroup$ Yes ! . These are only references to the original Verdier's work .It is well explained in the topological case in Cohomology of Sheaves (B.Iversen). Now Justin Curry himself says , in his "2012 paper" (mentioned by Carlo Beenakker in his answer)), that , when restrecting to f.g. stalks, the category equivalence between sheaves and cosheaves is contained in Verdier duality. . $\endgroup$
    – Al-Amrani
    Dec 18, 2014 at 19:41
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    $\begingroup$ Your comment does not change the fact that you are not answering the question which Mathieu Anel actually asked. $\endgroup$
    – Yemon Choi
    Dec 19, 2014 at 3:17

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