20 citations · 53 across the 15 of their papers we have counts for
20 papers
The universal property of strict polynomial functors
Antoine Touzé
In characteristic zero, the category of strict polynomial functors is well-known to be the tensor abelian category freely generated by one object. We show that this property fails…
On formality of diagrams of Eilenberg-MacLane spaces
Grigory Solomadin, Antoine Touzé
In this paper, we establish formality (over ) for diagrams of Eilenberg-MacLane spaces of any height . This implies spectral sequence (over ) colla…
Separation and excision in functor homology
Aurélien Djament, Antoine Touzé
We prove separation and excision results in functor homology. These results explain how the global Steinberg decomposition of functors proved by Djament, Touz{é} and Vespa behaves…
Homology of strict polynomial functors over Fp-linear additive categories
Aurélien Djament, Antoine Touzé
We generalize the strong comparison theorem of Franjou, Friedlander, Scorichenko and Suslin to the setting of Fp-linear additive categories. Our results have a strong impact in ter…
The homology of additive functors in prime characteristic
Aurélien Djament, Antoine Touzé
We compute certain Ext and Tor groups in the category of all functors from an Z/p-linear additive category A to vector spaces in terms of Ext and Tor computed in the full subcatego…
Functor homology over an additive category
Aurélien Djament, Antoine Touzé
We uncover several general phenomenas governing functor homology over additive categories. In particular, we generalize the strong comparison theorem of Franjou Friedlander Scorich…
Homological finiteness of functors on an additive category and applications
Aurélien Djament, Antoine Touzé
We give sufficient conditions which ensure that a functor of finite length from an additive category to finite-dimensional vector spaces has a projective resolution whose terms are…
Décompositions à la Steinberg sur une catégorie additive
Aurélien Djament, Antoine Touzé, Christine Vespa
We give a description of simple functors taking finitely generated values, from a small additive category to the category of vector spaces over a field. This result is analogous to…
Cohomology of algebraic groups with coefficients in twisted representations
Antoine Touzé
This article is a survey on the cohomology of a reductive algebraic group with coefficients in twisted representations. A large part of the paper is devoted to the advances obtaine…
On the structure of graded commutative exponential funtors
Antoine Touzé
We investigate the structure of graded commutative exponential functors. We give applications of these structure results, including computations of the homology of the symmetric gr…
Connectedness of cup products for polynomial representations of and applications
Antoine Touzé
We find conditions such that cup products induce isomorphisms in low degrees for extensions between stable polynomial representations of the general linear group. We apply this res…
Derived functors of the divided power functors
Lawrence Breen, Roman Mikhailov, Antoine Touzé
Some minor changes to the exposition.
A functorial control of integral torsion in homology
Antoine Touzé
We study the integral torsion of the values of strict polynomial functors defined over the integers. We interpret some classical homological invariants as values of strict polynomi…
Polynomial functors and categorifications of Fock space
Jiuzu Hong, Antoine Touzé, Oded Yacobi
Fix an infinite field of characteristic , and let $\g$ be the Kac-Moody algebra if and otherwise. Let $\PP$ denote the…
A construction of the universal classes for algebraic groups with the twisting spectral sequence
Antoine Touzé
In this article, we apply some ideas developped by M. Chałupnik to the framework of strict polynomial bifunctors. This allows us to get a new proof of the existence of the `univers…
Ringel duality and derivatives of non-additive functors
Antoine Touzé
We prove that Ringel duality in the category of strict polynomial functors can be interpreted as derived functors of non-additive functors (in the sense of Dold and Puppe). We give…
Bar complexes and extensions of classical exponential functors
Antoine Touzé
We compute Ext-groups between classical exponential functors (i.e. symmetric, exterior or divided powers) and their Frobenius twists. Our method relies on bar constructions, and br…
Cohomology of classical algebraic groups from the functorial viewpoint
Antoine Touzé
We prove that extension groups in strict polynomial functor categories compute the rational cohomology of classical algebraic groups. This result was previously known only for gene…
Bifunctor cohomology and Cohomological finite generation for reductive groups
Antoine Touzé, Wilberd van der Kallen
Let G be a reductive linear algebraic group over a field k. Let A be a finitely generated commutative k-algebra on which G acts rationally by k-algebra automorphisms. Invariant the…
Universal classes for algebraic groups
Antoine Touzé
We exhibit cocycles representing certain classes in the rational cohomology of of the general linear group with coefficients in the divided powers of a Frobenius twist of the adjoi…