Related papers: Hasse--Schmidt modules versus integrable connectio…

We study the rescalability of integrable mixed twistor $D$-modules. We prove some basic functoriality of the rescalability and the associated irregular Hodge filtration. We also observe that rescalable integrable mixed twistor $D$-modules…

In this work, we shall study in a purely model-independent fashion the $\infty$-category of mixed graded modules over a ring of characteristic $0$, and collect some basic results about its main formal properties. Finally, we shall endow…

Let $(R,\m)$ and $(S,\n)$ be commutative Noetherian local rings, and let $\phi:R\to S$ be a flat local homomorphism such that $\m S = \n$ and the induced map on residue fields $R/\m \to S/\n$ is an isomorphism. Given a finitely generated…

The aim of this note is to understand under which conditions invertible modules over a commutative S-algebra in the sense of Elmendorf, Kriz, Mandell and May give rise to elements in the algebraic Picard group of invertible graded modules…

Recently Tewari and van Willigenburg constructed modules of the 0-Hecke algebra that are mapped to the quasisymmetric Schur functions by the quasisymmetric characteristic and decomposed them into a direct sum of certain submodules. We show…

This paper studies the problems of embedding and isomorphism for countably generated Hilbert C*-modules over commutative C*-algebras. When the fibre dimensions differ sufficiently, relative to the dimension of the spectrum, we show that…

In this paper we study homological properties of modules over an affine Hecke algebra H. In particular we prove a comparison result for higher extensions of tempered modules when passing to the Schwartz algebra S, a certain topological…

A morphism of the moduli functor of admissible semistable pairs to the Gieseker -- Maruyama moduli functor (of semistable coherent torsion-free sheaves) with the same Hilbert polynomial on the surface, is constructed. It is shown that these…

Let k be an algebraically closed field of characteristic 0, and let $A = k[x,y]/(f)$ be a quasi-homogeneous plane curve. We show that for any graded torsion free A-module M, there exists a natural graded integrable connection, i.e. a graded…

Motivated by the need to relate the biparameter persistence module induced by a pair of scalar functions with the monoparameter persistence modules induced by each function separately, we introduce a construction that defines a kind of…

For a Specht module S^\lambda for the symmetric group \Sigma_d, the cohomology H^i(\Sigma_d, S^\lambda) is known only in degree i=0. We give a combinatorial criterion equivalent to the nonvanishing of the degree i=1 cohomology, valid in odd…

This work provides a unified formalism for studying difference and (Hasse-) differential algebraic geometry, by introducing a theory of "iterative Hasse rings and schemes". As an application, Hasse jet spaces are constructed generally,…

We classify integrable irreducible $\hat{g}[\sigma]$-modules in categories E and C, where E is proved to contain the well known evaluation modules and C to unify highest weight modules, evaluation modules and their tensor product modules.

We construct modules of the $0$-Hecke algebra whose images under the quasisymmetric characteristic map are the Young row-strict quasisymmetric Schur functions. This provides a representation-theoretic interpretation of this basis of…

We give a decomposition as a direct sum of indecomposable modules of several types of Specht modules in characteristic $2$. These include the Specht modules labelled by hooks, whose decomposability was considered by Murphy. Since the main…

For modules over a finite-dimensional algebra, there is a canonical one-to-one correspondence between the projective indecomposable modules and the simple modules. In this purely expository note, we take a straight-line path from the…

Consider a finite-dimensional algebra $A$ and any of its moduli spaces $\mathcal{M}(A,\mathbf{d})^{ss}_{\theta}$ of representations. We prove a decomposition theorem which relates any irreducible component of…

For a commutative Noetherian local ring we define and study the class of modules having reducible complexity, a class containing all modules of finite complete intersection dimension. Various properties of this class of modules are given,…

Previously, the last two authors found large families of decomposable Specht modules labelled by bihooks, over the Iwahori--Hecke algebra of type $B$. In most cases we conjectured that these were the only decomposable Specht modules…

We compare several classes of biparameter persistence modules: $\gamma$-products of monoparameter modules, hook-decomposable modules, modules admitting a Smith-type structure theorem, and modules of projective dimension at most 1. We…