Jon Carlson
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View article: Modules with finitely generated cohomology
Modules with finitely generated cohomology Open
Peer reviewed
View article: The ranks of homology of complexes of projective modules over finite groups
The ranks of homology of complexes of projective modules over finite groups Open
We show that counterexamples of Iyengar and Walker to the algebraic version of Gunnar Carlsson’s conjecture on the rank of the homology of a free complex can be extended to examples over any finite group with many choices of the complex.
View article: Locally dualizable modules abound
Locally dualizable modules abound Open
It is proved that given any prime ideal $\mathfrak{p}$ of height at least 2 in a countable commutative noetherian ring $A$, there are uncountably many more dualizable objects in the $\mathfrak{p}$-local $\mathfrak{p}$-torsion stratum of th…
View article: Modules with finitely generated cohomology
Modules with finitely generated cohomology Open
Let $G$ be a finite group and $\mathsf{k}$ a field of characteristic $p$. It is conjectured in a paper of the first author and John Greenlees that the thick subcategory of the stable module category StMod$(\mathsf{k}G)$ consisting of modul…
View article: The ranks of homology of complexes of projective modules over finite groups
The ranks of homology of complexes of projective modules over finite groups Open
We show that counterexamples of Iyengar and Walker to the algebraic version of Gunnar Carlsson's conjecture on the rank of the homology of a free complex can be extended to examples over any finite group with many choices of the complex.
View article: The endomorphism ring of the trivial module in a localized category
The endomorphism ring of the trivial module in a localized category Open
Suppose that $G$ is a finite group and $k$ is a field of characteristic $p >0$. Let $\mathcal{M}$ be the thick tensor ideal of finitely generated modules whose support variety is in a fixed subvariety $V$ of the projectivized prime ideal s…
View article: Idempotent modules, locus of compactness and local supports
Idempotent modules, locus of compactness and local supports Open
Let $kG$ be the group algebra of a finite group scheme defined over a field $k$ of characteristic $p>0$. Associated to any closed subset $V$ of the projectivized prime ideal spectrum $\operatorname{Proj} \operatorname{H}^*(G,k)$ is a thick…
View article: Torsion free endotrivial modules for finite groups of Lie type
Torsion free endotrivial modules for finite groups of Lie type Open
In this paper we determine the torsion free rank of the group of endotrivial\nmodules for any finite group of Lie type, in both defining and non-defining\ncharacteristic. On our way to proving this, we classify the maximal rank $2$\nelemen…
View article: The Neurostimulation Appropriateness Consensus Committee (NACC): Recommendations on Best Practices for Cervical Neurostimulation
The Neurostimulation Appropriateness Consensus Committee (NACC): Recommendations on Best Practices for Cervical Neurostimulation Open
View article: Bounded complexes of permutation modules
Bounded complexes of permutation modules Open
Let be a field of characteristic . For an elementary abelian -group, there exist collections of permutation modules such that if is any exact bounded complex whose terms are sums of copies of modules from the collection, then is contra…
View article: Nilpotence and duality in the complete cohomology of a module
Nilpotence and duality in the complete cohomology of a module Open
View article: Negative cohomology and the endomorphism ring of the trivial module
Negative cohomology and the endomorphism ring of the trivial module Open
Let $k$ be a field of characteristic $2$ and let $H$ be a finite group or group scheme. We show that the negative Tate cohomology ring $\widehat{\text{H}}^{\leq 0}(H,k)$ can be realized as the endomorphism ring of the trivial module in a V…
View article: Torsion Free Endotrivial Modules for Finite Groups of Lie Type
Torsion Free Endotrivial Modules for Finite Groups of Lie Type Open
In this paper we determine the torsion free rank of the group of endotrivial modules for any finite group of Lie type, in both defining and non-defining characteristic. On our way to proving this, we classify the maximal rank $2$ elementar…
View article: Relatively Projectivity and the Green correspondence for complexes
Relatively Projectivity and the Green correspondence for complexes Open
We investigate a version of the Green correspondence for categories of complexes, including homotopy categories and derived categories. The correspondence is an equivalence between a category defined over a finite group $G$ and the same fo…
View article: Decoupling of Kimberlite Source and Primitive Melt Compositions
Decoupling of Kimberlite Source and Primitive Melt Compositions Open
View article: Geometric and Topological Aspects of the Representation Theory of Finite Groups
Geometric and Topological Aspects of the Representation Theory of Finite Groups Open
View article: Separable Commutative Rings in the Stable Module Category of Cyclic Groups
Separable Commutative Rings in the Stable Module Category of Cyclic Groups Open
View article: Separable commutative rings in the stable module category of cyclic groups
Separable commutative rings in the stable module category of cyclic groups Open
We prove that the only separable commutative ring-objects in the stable module category of a finite cyclic p-group G are the ones corresponding to subgroups of G. We also describe the tensor-closure of the Kelly radical of the module categ…
View article: Hopf algebra structures and tensor products for group algebras
Hopf algebra structures and tensor products for group algebras Open
The modular group algebra of an elementary abelian p-group is isomorphic to the restricted enveloping algebra of commutative restricted Lie algebra. The different ways of regarding this algebra result in different Hopf algebra structures t…
View article: THE GRADED CENTER OF A TRIANGULATED CATEGORY
THE GRADED CENTER OF A TRIANGULATED CATEGORY Open
With applications in mind to the representations and cohomology of block algebras, we examine elements of the graded center of a triangulated category when the category has a Serre functor. These are natural transformations from the identi…
View article: Ghosts and Strong Ghosts in the Stable Category
Ghosts and Strong Ghosts in the Stable Category Open
Suppose that $G$ is a finite group and $k$ is a field of characteristic $p>0$. A ghost map is a map in the stable category of finitely generated $kG$-modules which induces the zero map in Tate cohomology in all degrees. In an earlier paper…
View article: Ghosts and Strong Ghosts in the Stable Module Category
Ghosts and Strong Ghosts in the Stable Module Category Open
Suppose that $G$ is a finite group and $k$ is a field of characteristic $p>0$. A ghost map is a map in the stable category of finitely generated $kG$-modules which induces the zero map in Tate cohomology in all degrees. In an earlier paper…
View article: Endotrivial Modules for Finite Groups of Lie Type A in Nondefining\n Characteristic
Endotrivial Modules for Finite Groups of Lie Type A in Nondefining\n Characteristic Open
Let $G$ be a finite group such that $\\text{SL}(n,q)\\subseteq G \\subseteq\n\\text{GL}(n,q)$ and $Z$ be a central subgroup of $G$. In this paper we\ndetermine the group $T(G/Z)$ consisting of the equivalence classes of\nendotrivial $k(G/Z…
View article: Endotrivial Modules for Finite Groups of Lie Type A in Nondefining Characteristic
Endotrivial Modules for Finite Groups of Lie Type A in Nondefining Characteristic Open
Let $G$ be a finite group such that $\text{SL}(n,q)\subseteq G \subseteq \text{GL}(n,q)$ and $Z$ be a central subgroup of $G$. In this paper we determine the group $T(G/Z)$ consisting of the equivalence classes of endotrivial $k(G/Z)$-modu…