Related papers: Relative Hom-Hopf modules and total integrals

We prove that for any proper smooth formal scheme $\frak X$ over $\mathcal O_K$, where $\mathcal O_K$ is the ring of integers in a complete discretely valued nonarchimedean extension $K$ of $\mathbb Q_p$ with perfect residue field $k$ and…

Given a a Hopf algebra $H$, its left coideal subalgebra $A$ and a non-zero multiplicative functional $\mu$ on $A$, we define the space of left $\mu$-integrals $L^A_\mu\subset A$. We observe that $\dim L^A_\mu=1$ if $A$ is a Frobenius…

Let $I$ denote an ideal in a commutative Noetherian ring $R$. Let $M$ be an $R$-module. The $I$-adic completion is defined by $\hat{M}^I = \varprojlim{}_{\alpha} M/I^{\alpha}M$. Then $M$ is called $I$-adic complete whenever the natural…

We construct a perfect version of Morel--Voevodsky's motivic homotopy category over a perfect base scheme in positive characteristic. By checking the axioms of a coefficient system, we establish a six-functor formalism. We show that…

Let $\frak a$ be an ideal of a commutative noetherian ring $R$ with unity and $M$ an $R$-module supported at $\V(\fa)$. Let $n$ be the supermum of the integers $i$ for which $H^{\fa}_i(M)\neq 0$. We show that $M$ is $\fa$-cofinite if and…

Given a finitely generated and projective Lie-Rinehart algebra, we show that there is a continuous homomorphism of complete commutative Hopf algebroids between the completion of the finite dual of its universal enveloping Hopf algebroid and…

Let H be a Hopf algebra. By definition a modular crossed H-module is a vector space M on which H acts and coacts in a compatible way. To every modular crossed H-module M we associate a cyclic object Z(H,M). The cyclic homology of Z(H,M)…

Any multiplier Hopf *-algebra} with positive integrals gives rise to a locally compact quantum group (in the sense of Kustermans and Vaes). As a special case of such a situation, we have the compact quantum groups (in the sense of…

In this paper, we introduce and investigate \emph{bisemialgebras}and\emph{\ Hopf semialgebras} over commutative semirings. We generalize to the semialgebraic context several results on bialgebras and Hopf algebras over rings including the…

Let $(A,\Delta)$ be a locally compact quantum group and $(A_0,\Delta_0)$ a regular multiplier Hopf algebra. We show that if $(A_0,\Delta_0)$ can in some sense be imbedded in $(A,\Delta)$, then $A_0$ will inherit some of the analytic…

Let $k$ be a commutative ring, $H$ a faithfully flat Hopf algebra with bijective antipode, $A$ a $k$-flat right $H$-comodule algebra. We investigate when a relative Hopf module is projective over the subring of coinvariants $B=A^{{\rm…

Let $B$ and $C$ be non-degenerate idempotent algebras and assume that $E$ is a regular separability idempotent in $M(B\otimes C)$. Define $A=C\otimes B$ and $\Delta:A\to M(A\otimes A)$ by $\Delta(c\otimes b)=c\otimes E\otimes b$. The pair…

We consider the adjoint representation of a Hopf algebra $H$ focusing on the locally finite part, $H_{\text{adfin}}$, defined as the sum of all finite-dimensional subrepresentations. For virtually cocommutative $H$ (i.e., $H$ is finitely…

There appeared not long ago a Reduction Formula for derived Hochschild cohomology, that has been useful e.g., in the study of Gorenstein maps and of rigidity w.r.t. semidualizing complexes. The formula involves the relative dualizing…

A strict 2-group is a 2-category with one object in which all morphisms and all 2-morphisms have inverses. 2-Groups have been studied in the context of homotopy theory, higher gauge theory and Topological Quantum Field Theory (TQFT). In the…

We construct a category $\mathrm{HomCob}$ whose objects are {\it homotopically 1-finitely generated} topological spaces, and whose morphisms are {\it cofibrant cospans}. Given a manifold submanifold pair $(M,A)$, we prove that there exists…

A key result in a 2004 paper by S. Arkhipov, R. Bezrukavnikov, and V. Ginzburg compares the bounded derived category of modules for the principal block of a Lusztig quantum enveloping algebra at anroot of unity with an explicit subcategory…

Holm (H. Holm, Modules with cosupport and injective functors, Algebr. Represent. Theor., 13 (2010), 543-560) considers categories of right modules dual to those with support in a set of finitely presented modules. We extend some of his…

We develop a theory of \emph{locally Frobenius algebras} which are colimits of certain directed systems of Frobenius algebras. A major goal is to obtain analogues of the work of Moore \& Peterson and Margolis on \emph{nearly Frobenius…

We prove a series of Approximation Theorems in the setting of Waldhausen quasicategories. These theorems, inspired by Waldhausen's 1985 Approximation Theorem, give sufficient conditions for an exact functor of Waldhausen quasicategories to…