## How to glue perverse sheaves.(English)Zbl 0651.14009

$$K$$-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

Zbl 0621.00010