Jul 2026· Algebras and Representation Theory· 0 citations· 14 references
Abstract
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We provide an equivariant extension of Carlsson’s BGG correspondence in characteristic two. As an application we classify perfect cochain complexes of
<jats:inline-formula>
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<jats:tex-math>$$(\mathbb {Z}/2\times \mathbb {Z}/2)\rtimes Q$$</jats:tex-math>
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<mml:mn>2</mml:mn>
<mml:mo>×</mml:mo>
<mml:mi>Z</mml:mi>
<mml:mo>/</mml:mo>
<mml:mn>2</mml:mn>
<mml:mo>)</mml:mo>
<mml:mo>⋊</mml:mo>
<mml:mi>Q</mml:mi>
</mml:mrow>
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-representations with four-dimensional total homology for finite groups
<jats:italic>Q</jats:italic>
of odd order. We deduce that cochain complexes of finite, free
<jats:inline-formula>
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<jats:tex-math>$$A_4$$</jats:tex-math>
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<mml:mi>A</mml:mi>
<mml:mn>4</mml:mn>
</mml:msub>
</mml:math>
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-CW complexes with four-dimensional total homology are rigid: They are determined by the degrees of the nonzero homology groups.
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We bound the total variation distance in the Kubilius model for sequences with positive level of distribution. We obtain a result that we expect is qualitatively optimal. As a special case, it recovers a recent result of Ford on shifted primes, with a slightly simplified...
Using Galois covering theory and equivariant techniques, we classify all connected representation-tame Gei\ss--Leclerc--Schr\"oer (GLS) algebras in terms of their defining triples $(C,D,\Omega)$. We then study the GLS algebras $H(\widetilde{CD}_n)$ with minimal symmetrizers, where $n\geq 2$ and $\widetilde{CD}_2=\widet...
Qiang Dong, Zeng-Qiang Lin, Ming Lu et al.· 0 citations
In this article we generalise a classical Kolyvagin's result on the vanishing of the $p$-part of the Shafarevich--Tate group of an elliptic curve (defined over $\mathbb{Q}$) over an imaginary quadratic field $K$ to modular abelian varieties of $\mathrm{GL}_2$-type (defined over a totally real number field $F$) and a CM...
Luca Mastella, Ahmed Matar, Francesco Zerman· 0 citations
For $k\geq1$, let $M_k=[(z-w)^k]\subset H^2(\mathbb D^2)$. We first determine the banded Toeplitz matrices associated with the homogeneous components of $M_k$, together with explicit formulas for their determinants and the relevant algebraic cofactors. These formulas lead to a complete description of the spectrum of th...
Let $F=\mathbb{F}_q((u))((t))$ and $H=\mathrm{GL}_n(F)_L\times\mathrm{GL}_n(F)_R$. An ordered tuple $\alpha=(\alpha_1,\dots, \alpha_n) $ defines a cross-$K_2$ multiplier on the doubled Borel. Twisted equivariantization then yields an exact uniformly smooth categorical principal series $2$-representation of $H$. For uni...
For $k\ge 2$, let $M_k=[z^k-w^k]$ be the principal homogeneous submodule of the Hardy space over the bidisk. We determine Yang's complete sequence of numerical invariants and prove $$ \Sigma_0(M_k)=\frac{\pi^2}{6},\qquad \Sigma_j(M_k)=\Sigma_{\lceil j/k\rceil}([z-w]),\quad j\ge1. $$ The proof exploits a residue-class d...
Yin Liu, Yu-Feng Lu, Chao Zu· 1 citation
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