ABSTRACT
Let be the Springer resolution of the nilpotent cone for a semisimple connected algebraic group G over ℂ and k be an arbitrary field. What happens to
if the decomposition theorem fails for it? We show that in this case, some additional (with respect to the case char k=0) composition factors of this direct image in the (abelian) category of perverse sheaves may emerge. These factors emerge from the
-composition factors of the radicals of certain intersection forms and from that of the top cohomologies of Springer fibres (in the non-semisimple case).
MATHEMATICS SUBJECT CLASSIFICATION:
Notes
1Use the shifted versions δ(a)⋅B and δ(a)⋅A of B and A, respectively.
2Use the shifted versions c⋅B and c⋅A of B and A, respectively.
3Part (1) corresponds to , part (2) to
and part (3) to
.