相关论文: Compairing categories of Lubin-Tate $(\varphi_L,\G…

We describe equivalence classes of exact indecomposable module categories over a finite graded tensor category. When applied to a pointed fusion category, our results coincide with the ones obtained in [S. Natale, On the equivalence of…

Degeneration of modules is usually defined geometrically, but due to results of Zwara and Riedtmann we can also define it in terms of exact sequences. This definition also works over fields that are not algebraically closed. Let $k$ be a…

We introduce a class of topologies on the Leavitt path algebra $L(\Gamma)$ of a finite directed graph and decompose a graded completion $\widehat{L}(\Gamma)$ as a direct sum of minimal ideals.

By means of an appropriate re-scaling of the metric in a Lagrangian, we are able to reduce it to a kinetic term only. This form enables us to examine the extended complexified solution set (complex moduli space) of field theories by finding…

The cohomology of the Lubin-Tate tower is known to realize the local Langlands correspondence for GL(n) over a nonarchimedean local field. In this article we make progress towards a purely local proof of this fact. To wit, we find a family…

We classify thick subcategories of the $\infty$-categories of perfect modules over ring spectra which arise as functions on even periodic derived stacks satisfying affineness and regularity conditions. For example, we show that the thick…

Let $\mathcal{R}$ be a free Lie conformal algebra of rank $2$ with $\mathbb{C}[\partial]$-basis $\{L,I\}$ and relations \begin{eqnarray*} \left[L_{\lambda} L\right]=(\partial+2 \lambda) (L+I),\ \left[L_{\lambda} I\right]=(\partial+\lambda)…

Using the non-semisimple Temperley-Lieb calculus, we study the additive and monoidal structure of the category of tilting modules for $\mathrm{SL}_{2}$ in the mixed case. This simultaneously generalizes the semisimple situation, the case of…

Let $L/K$ be a finite Galois extension of fields with group $\Gamma$. When $\Gamma$ is nilpotent, we show that the problem of enumerating all nilpotent Hopf-Galois structures on $L/K$ can be reduced to the corresponding problem for the…

We give a category theoretic approach to several known equivalences from (classic) tilting theory and commutative algebra. Furthermore, we apply our main results to establish a duality theory for relative Cohen-Macaulay modules in the sense…

We give explicit structure of the graded ring of modular forms with respect to Gamma(N) (N=1,2,3,4,5,6,7,8,9,10,12,16,18) and for some other congruence groups. We also study the modular forms of half-integer weight for certain groups.

We study the triangulated subcategories of compact objects in stable homotopy categories such as the homotopy category of spectra, the derived categories of rings, and the stable module categories of Hopf algebras. In the first part of this…

The goal of this article is to propose and examine the notion of graded classical weakly prime submodules over non-commutative graded rings which is a generalization of the concept of graded classical weakly prime submodules over…

Let K be a finite unramified extension of Q_p. We parametrize the (phi, Gamma)-modules corresponding to reducible two-dimensional mod p representations of G_K and characterize those which have reducible crystalline lifts with certain…

A class of non-semisimple extensions of Lie superalgebras is studied. They are obtained by adjoining to the superalgebra its adjoint representation as an abelian ideal. When the superalgebra is of affine Kac-Moody type, a generalisation of…

We study modular forms of some congruence subgroups. In this paper, we treat the cases level is 2-power, 3-power or 5. Structures of graded rings and many identities of infinite sum or infinite product are given. Theory of rational (1/3,…

We prove a finiteness result for the p-adic cohomology of the Lubin-Tate tower. For any n>=1 and p-adic field F, this provides a canonical functor from admissible p-adic representations of GL_n(F) towards admissible p-adic representations…

The aim of this article is to study basic structures and interrelations of $\delta$-rings, perfectoid towers, and lim Cohen-Macaulay sequences over Noetherian rings in positive or mixed characteristic. Then we discuss some methods for…

Let $\mathcal{W}(b)$ be a class of free Lie conformal algebras of rank $2$ with $\mathbb{C}[\partial]$-basis ${L,H}$ and relations \begin{eqnarray*} [L_\lambda L]=(\partial+2\lambda)L,\ \ [L_\lambda H]=\big(\partial+(1-b)\lambda\big)H, \ \…

We generalise to a group homomorphism $\tau$ the $\chi$-graded categories of S\"{o}zer and Virelizier. These are categories in which both morphisms and objects have compatible degrees. We give a 'half-enriched' Yoneda lemma, a structure…