2
$\begingroup$

Hello,

Can anybody point to me a reference about the preservation of the derived bounded category of sheaves with constructible cohomology on the underlying classical (anayltic) space of a complex algebraic variety, with respect to the functors Verdier duality and push-forward (probably "!").

Note that I am aware of Kashiwara and Schapira book, but I would like some other reference which does not use this microlocalization things which I do not know.

Thank you, Sasha

$\endgroup$

2 Answers 2

2
$\begingroup$

You could try Sheaves in Topology by Alexandru Dimca. There are no prerequisites other than basic sheaf theory, so you don't have to worry about microlocal troubles or anything else.

$\endgroup$
2
  • 3
    $\begingroup$ I like this book a lot, but (like for most 'heavy' results) it doesn't actually give a proof, only references. Here is what Dimca writes immediately before Theorem 4.1.5., which says that $D^b_c(-)$ is closed under the six operations: "For the proof in the case X, Y smooth, see [Kashiwara and Schapira]. The singular case follows from [Borel], see also remark 4.1.7. below. The claim in (i)(b), the algebraic case, is in [Nori]. For a unified treatment, see [Schürmann]." $\endgroup$ Jan 26, 2012 at 10:30
  • $\begingroup$ I could not find no where [Nori] though (not in my library, nor online). $\endgroup$
    – Sasha
    Jan 26, 2012 at 12:08
0
$\begingroup$

There is a new book Perverse Sheaves and Applications to Representation Theory by Pramod N. Achar, which is published in 2021. I think it contains all details you need and it does not use microlocal method.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.