REVIEW 2 cited by
$\mathrm{VI}$ modules in non-describing characteristic, Part I
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
abstract
Let $\mathrm{VI}$ be the category of finite dimensional $\mathbb{F}_q$-vector spaces whose morphisms are injective linear maps, and let $\mathbf{k}$ be a noetherian ring. We study the category of functors from $\mathrm{VI}$ to $\mathbf{k}$-modules in the case when $q$ is invertible in $\mathbf{k}$. Our results include a structure theorem, finiteness of regularity, and a description of the Hilbert series. These results are crucial in the classification of smooth irreducible $\mathbf{GL}_{\infty}(\mathbb{F}_q)$-representations in non-describing characterisitic which is contained in Part II of this paper.
Forward citations
Cited by 2 Pith papers
-
GL-algebras in positive characteristic III: the divided power algebra
The divided power algebra Div(k^∞) over a field of characteristic p is GL-coherent, and its bounded derived category of finitely presented modules has a semi-orthogonal decomposition into pieces generated by D^(r) ⊗ L_λ.
-
A torsion theoretic interpretation for sheaves of modules and Grothendieck topologies on directed categories
Sheaves of modules are exactly the J-saturated presheaves, every Grothendieck topology on a noetherian EI directed category is rigid, and all topologies on type N/Z categories are classified.
Discussion (0). Continue with ORCID to comment.