How to glue perverse sheaves. (English) Zbl 0651.14009

Beilinson, A. A.

\(K\)-theory, arithmetic and geometry, Semin., Moscow Univ. 1984-86, Lect. Notes Math. 1289, 42-51 (1987).

[For the entire collection see Zbl 0621.00010.]
The note describes glueing data for middle perverse sheaves in the situation of a scheme X, a function f on X, \(Y=f^{-1}(0)\) and \(U=X-Y\). The data are sheaves \(M_ U\), \(M_ Y\) together with mappings between \(M_ Y\) and the nearby cycles sheaf of \(M_ U\). The method is based on a description of the unipotent part of the nearby-cycles functor by Jordan blocks.

Reviewer: G.Horrocks

MSC:

14F05	Sheaves, derived categories of sheaves, etc. (MSC2010)
14F40	de Rham cohomology and algebraic geometry

Keywords:

middle perverse sheaves; nearby cycles sheaf

Citations:

Zbl 0621.00010