Title:
A propos d'une question de Friedlander et Suslin I --
Une r'esolution injective des puissances sym'etriques twist'ees
(in French)
Author: Alain Troesch
AMS Classification Numbers: 18G05, 18G10, 18G35, 55U05
Address of Author: Institut de Mathematiques de Jussieu, Case 82
4 place Jussieu, F-75252 PARIS CEDEX 05
e-mail address: troesch@math.jussieu.fr
Abstract.
Some years ago, Friedlander and Suslin constructed an explicit
injective resolution of twisted symmetric powers in the category of
strict polynomial functors over a ground field of characteristic
2. The factors in this resolutions are given by direct sums of tensor
products of (non twisted) symmetric powers. The case of a symmetric
power twisted only once is a well-known result: it is some kind of
Koszul complex.
In characteritic p>2, nothing similar was known up to now, even for a
single twist. In this paper, we construct such injective
resolutions. The resolutions we construct are in fact "p-resolutions",
that is, the differential does not vanish when composed twice, but
only when composed p times.
This result should unable us to constuct an injective resolution of
any twisted functor if we know an injective resolution of the
corresponding non twisted functor. This will be the subject of another
paper.