Related papers: Modules and Infinitary Logics

Let $G$ be a finite group, and let $V$ be a completely reducible faithful $G$-module. It has been known for a long time that if $G$ is abelian, then $G$ has a regular orbit on $V$. In this paper we show that $G$ has an orbit of size at…

We determine all of lines in the moduli space $M$ of stable bundles for arbitrary rank and degree. A further application of minimal rational curves is also given in last section.

We investigate whether the group algebra of a finite group over a localisation of the integers is semiperfect. The main result is a necessary and sufficient arithmetic criterion in the ordinary case. In the modular case, we propose a…

Simple-minded systems in stable module categories are defined by orthogonality and generating properties so that the images of the simple modules under a stable equivalence form such a system. Simple-minded systems are shown to be invariant…

We explore the integration of representations from a Lie algebra to its algebraic group in positive characteristic. An integrable module is stable under the twists by group elements. Our aim is to investigate cohomological obstructions for…

We prove the modularity of a positive proportion of abelian surfaces over $\mathbf{Q}$. More precisely, we prove the modularity of abelian surfaces which are ordinary at $3$ and are $3$-distinguished, subject to some assumptions on the…

We generalize the validity criterion for the infinitary proof system of the multiplicative additive linear logic with fixed points. Our criterion is designed to take into account axioms and cuts. We show that it is sound and enjoys the cut…

We show some preservation results of amenably extending strongly Ulam stable groups under mild decay assumptions, including quantitative preservation of asymptotic bounds under the assumption that the modulus of stability is H\"older…

We prove that an abelian category equipped with an ample sequence of objects is equivalent to the quotient of the category of coherent modules over the corresponding algebra by the subcategory of finite-dimensional modules. In the…

In this article, we prove that induced modules of support $\tau$-tilting modules over blocks of finite groups satisfying inertial-invariant condition are also support $\tau$-tilting modules.

In this paper we study families of representations of the outer automorphism groups indexed on a collection of finite groups $\mathcal{U}$. We encode this large amount of data into a convenient abelian category $\mathcal{A}\mathcal{U}$…

We adapt Grayson's model of higher algebraic $K$-theory using binary acyclic complexes to the setting of stable $\infty$-categories. As an application, we prove that the $K$-theory of stable $\infty$-categories preserves infinite products.

In this work we study a kind of coherence condition on FI_G-modules, which generalizes the usual notion of finite generation. We prove that a module is coherent, in the appropriate sense, if and only if its generators, as well as its…

We study infinite string modules that are bricks over some gentle algebras. In particular, we first give a complete classification of these modules over the double-Kronecker gentle algebra and prove that each family is in bijection with a…

Hybrid logic extends modal logic with special propositions called nominals, each of which is true at only one state in a model. This enables us to describe some properties of binary relations, such as irreflexivity and anti-symmetry, which…

We prove that, up to adding a complement, every modular representation of a finite group admits a finite resolution by permutation modules.

We define an unstable equivariant motivic homotopy category for an algebraic group over a Noetherian base scheme. We show that equivariant algebraic $K$-theory is representable in the resulting homotopy category. Additionally, we establish…

Let $R$ be an algebra over a ring $\Bbbk$, $T$ an $R$-algebra, $M$ a finitely generated projective $R$-module, and $N$ a $T$-module. Let $G$ be a linearly reductive group scheme over $\Bbbk$ equipped with a representation…

We study group extensions of Finite Abelian Groups using matrices. We also prove a Theorem for equivalence of extensions using matrices.

It is a known fact that any unimodular equation over an abelian group has a solution in that group itself. It is also known that for metabelian groups this does not hold; moreover, there is a unimodular equation over some metabelian group…