Une résolution injective des puissances symétriques tordues

Ext-groups in the Category of Strict Polynomial Functors

“…The second ingredient that we use to prove Theorem 4.2.5 is the explicit injective coresolution T of I (r) constructed by Friedlander-Suslin [10] if p = 2 and by Troesch [24] in general case. This idea of using this coresolution of Troesch to compute Ext-groups in the category of the strict polynomial functors is due to Touzé, see [21].…”

“…, µ p r −1 ) such that p r −1 j=0 µ j = p r and p r −1 j=0 jµ j = p r i 2 + p r−1 i − 2 i 2 . By [24], the part of cohomological degree i of the complex T is T i = µ∈I(i) S µ .…”

“…The Troesch coresolutions [24] of the functors S d(r) are p r -coresolutions. Thus we deduce the following result.…”

Additive polynomial superfunctors and cohomology

“…This is to say, we aim to search some super analogues of the universal classes constructed in [13] and use them to produce the isomorphism of the conjecture by means of cup products, in a similar way as we have defined the isomorphism of Theorem 1.1. The construction of the universal classes made by Touzé relied on the use of Troesch p-complexes, introduced in [14]. To find these super classes one should then investigate the "superized" Troesch complex recently constructed by Drupieski and Kujawa [4].…”

Superized Troesch complexes and cohomology for strict polynomial superfunctors

“…In the case n = 1, this injective resolution permitted an easy calculation of Ext • P (I (r) , I (r) ). Later, Troesch [20] showed that Friedlander and Suslin's construction could be generalized to odd characteristics, but at the cost that the underlying object of the construction was no longer a chain complex in the ordinary sense. Rather, it is a p-complex, i.e., a graded object C • equipped with a map d : C i → C i+1 such that d p = 0 instead of the usual d 2 = 0.…”