Related papers: The reductive Borel-Serre compactification as a mo…

Given a finitely generated module $M$ over a commutative local ring (or a standard graded $k$-algebra) $(R,\m,k) $ we detect its complexity in terms of numerical invariants coming from suitable $\m$-stable filtrations $\mathbb{M}$ on $M$.…

For a smooth quasi-projective surface S over complex numbers we consider the Borel-Moore homology of the stack of coherent sheaves on S with compact support and make this space into an associative algebra by a version of the Hall…

Greenlees has conjectured that the rational stable equivariant homotopy category of a compact Lie group always has an algebraic model. Based on this idea, we show that the category of rational local systems on a connected finite loop space…

The monomorphism category $\mathscr{S}(A, M, B)$ induced by a bimodule $_AM_B$ is the subcategory of $\Lambda$-mod consisting of $\left[\begin{smallmatrix} X\\ Y\end{smallmatrix}\right]_{\phi}$ such that $\phi: M\otimes_B Y\rightarrow X$ is…

A categorical approach to linear control systems is introduced. Feedback actions on linear systems arises as a symmetric monoidal category. Stable feedback isomorphisms generalize enlargement of pairs of matrices. Subcategory of locally…

We show that Mandell's inverse $K$-theory functor is a categorically-enriched non-symmetric multifunctor. In particular, it preserves algebraic structures parametrized by non-symmetric operads. As applications, we describe how ring…

In this paper, we consider the endomorphism algebras of infinitely generated tilting modules of the form $R_{\mathcal U}\oplus R_{\mathcal U}/R$ over tame hereditary $k$-algebras $R$ with $k$ an arbitrary field, where $R_{\mathcal{U}}$ is…

We prove that in a locally finite dimensional Lie algebra L, any maximal, locally solvable subalgebra (Borel subalgebra) is the stabilizer of a maximal, generalized flag in an integrable, faithful module over L.

We show that for algebraic groups over local fields of characteristic zero, the following are equivalent: Every homomorphism has a closed image, every unitary representation decomposes into a direct sum of finite-dimensional and mixing…

For an odd-dimensional oriented hyperbolic manifold with cusps and strongly acyclic coefficient systems we define the Reidemeister torsion of the Borel-Serre compactification of the manifold using bases of cohomology classes defined via…

We develop a "Soergel theory" for Bruhat-constructible perverse sheaves on the flag variety $G/B$ of a complex reductive group $G$, with coefficients in an arbitrary field $\Bbbk$. Namely, we describe the endomorphisms of the projective…

Let X be the locally symmetric space associated to a reductive $\mathbb Q$-group G and an arithmetic subgroup $\Gamma$. An L-module M is a combinatorial model of a constructible complex of sheaves on $\widehat X$, the reductive Borel-Serre…

We define united KK-theory for real C*-algebras A and B such that A is separable and B is sigma-unital, extending united K-theory in the sense that KK\crt(\R, B) = K\crt(B). United KK-theory contains real, complex, and self-conjugate…

The aim of this paper is to give a proof of the restriction theorems for principal bundles with a reductive algebraic group as structure group in arbitrary characteristic. Let $G$ be a reductive algebraic group over any field $k=\bar{k}$,…

Equivariant homotopy methods developed over the last 20 years lead to recent breakthroughs in the Borel isomorphism conjectures for Loday assembly maps in K- and L-theories. An important consequence of these algebraic conjectures is the…

Let $k$ be a field. In this paper, we define the notion of semi-fiber products of commutative $k$-algebras and show that the class of such rings contains several classes of commutative rings, including that of the fiber products of local…

Given a ring $R$, we have a classical result stating that the ordinary category of modules is the abelianization of the category of augmented $R$-algebras. Analogously, using the framework of infinity categories and higher algebra, Francis…

The original Bondi$-$Metzner-Sachs (BMS) group B is the common asymptotic symmetry group of all asymptotically flat Lorentzian 4-dim space$-$times. As such, B is the best candidate for the universal symmetry group of General Relativity…

We describe the algebraic K-theory of the $K(1)$-local sphere and the category of type 2 finite spectra in terms of K-theory of discrete rings and topological cyclic homology. We find an infinite family of 2-torsion classes in the $K_0$ of…

We consider spatial discretizations by the finite section method of the restricted group algebra of a finitely generated discrete group, which is represented as a concrete operator algebra via its left-regular representation. Special…