nLab
perverse sheaf

Outline

To a space (typically with singularities) of certain kind (there are variants) one associates category whose objects are called perverse sheaves. They are neither perverse nor sheaves; but they are related to some sheaf categories and notably generalize the intersection cohomology. Perversity is there a parameter involved in grading of intersection cohomology groups. Another feature similar to sheaves is that they are somehow determined by the local data; there is a famous gluing due Sasha Beilinson. In one of the approaches (see MacPherson’s notes) there are even modified Steenrod-Eilenberg axioms stated for intersection cohomology.

References

  • A. A. Beilinson, J. Bernstein, P. Deligne, Faisceaux pervers, Astérisque 100 (1980) MR86g:32015

  • scan of old notes from MacPherson pdf

  • Reinhardt Kiehl, Rainer Weissauer, Weil conjectures, perverse sheaves and l’adic Fourier transform, Ergebnisse Der Mathematik Und Ihrer Grenzgebiete 42, Springer 2001.

  • Mark Andrea de Cataldo, Luca Migliorini, What is a perverse sheaf ?, arxiv/1004.2983, Notices of Amer. Math. Soc. May 2010, pdf

  • Ryan Reich, Notes on Beilinson’s “How to glue perverse sheaves”, arxiv/1002.1686

Revised on March 6, 2013 19:43:22 by Zoran Škoda (161.53.130.104)