Timeline for Cohomology of constructible sheaves via exit paths
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| Jan 2, 2023 at 13:38 | comment | added | Markus Zetto | See math.ias.edu/~lurie/287xnotes/Lecture26.pdf for the non-stratified analogue (use the Dold-Kan correspondence); e.g. the right adjoint is similar to a (automatically derived) global sections functor. Also, note how this construction works for every stratified map, not only the terminal one. Applying Verdier duality further yields versions of Borel-Moore homology and cptly. supp. cohomology. Finally, your idea about gluing from local systems sounds very reasonable on the level of cochains; I'll try to figure out a precise statement. | |
| Jan 2, 2023 at 13:27 | comment | added | Markus Zetto | For $X \to P$ a stratified space that satisfies the exodromy equivalence for constructible $\infty$-sheaves, the terminal map $X \to *$ induces the terminal map $\operatorname{Sing}^P(X) \to *$ on exit-path $\infty$-categories, which again induces, by left and right Kan extension, an adjoint triple between the categories of constructible sheaves on $X$ and on $*$. The latter is however just the coefficient category. I would claim that the left Kan extension $C_*$ agrees with homology with coefficients in the constructible sheaf and the right Kan extension $C^*$ with cohomology. | |
| Apr 14, 2020 at 15:57 | comment | added | Tim Porter | Have you looked in Lurie's draft book: Higher Algebra in Appendix A. math.ias.edu/~lurie/papers/HA.pdf and the various works that cite that source? | |
| Apr 14, 2020 at 13:54 | comment | added | Denis Nardin | For your side question, I guess the canonical answer is this paper | |
| Apr 14, 2020 at 8:01 | history | asked | Patrick Elliott | CC BY-SA 4.0 |