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Perverse Sheaves

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Intersection Homology & Perverse Sheaves

Part of the book series: Graduate Texts in Mathematics ((GTM,volume 281))

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Abstract

Perverse sheaves are fundamental objects of study in topology, algebraic geometry, analysis and differential equations, with a plethora of applications, including in adjacent fields such as number theory, representation theory, combinatorics and algebra. In this chapter, we overview the relevant definitions and results of the theory of perverse sheaves, with an emphasis on examples and applications (see also Chapters 9 and 10 for more applications of perverse sheaves).

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Notes

  1. 1.

    Strictly full means that if F ∈ D and G ∈ D ≀0, and F≅G in D, then F ∈ D ≀0.

  2. 2.

    Turning a triangle refers to the fact that \(P' \to P \to P'' \overset {[1]} \to \) is a distinguished triangle if and only if \(P \to P'' \to P'[1] \overset {[1]} \to \) is a distinguished triangle.

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Authors and Affiliations

  1. Department of Mathematics, University of Wisconsin-Madison, Madison, WI, USA

    Laurenţiu G. Maxim

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  1. Laurenţiu G. Maxim
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Maxim, L.G. (2019). Perverse Sheaves. In: Intersection Homology & Perverse Sheaves. Graduate Texts in Mathematics, vol 281. Springer, Cham. https://doi.org/10.1007/978-3-030-27644-7_8

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