Related papers: Duality between injective envelopes and flat cover…

We present a new proof of the sphere covering inequality in the spirit of comparison geometry, and as a byproduct we find another sphere covering inequality which can be viewed as the dual of the original one. We also prove sphere covering…

Let $A$ be a unital $C^*$-algebra. We call an $A$-multiplier cover a pair $(E,\iota)$ consisting of a $C^*$-algebra $E$ and a faithful non-degenerate $*$-homomorphism $\iota\colon A\to M(E)$. Ordering such covers by $A$-preserving unital…

We classify 1-dimensional connected dually flat manifolds $M$ that are toric in the sense of [Molitor, arXiv:2109.04839], and show that the corresponding torifications are complex space forms. Special emphasis is put on the case where M is…

We present a duality between the category of compact Riemannian spin manifolds (equipped with a given spin bundle and charge conjugation) with isometries as morphisms and a suitable "metric" category of spectral triples over commutative…

We define a new algebra of noncommutative differential forms for any Hopf algebra with an invertible antipode. We prove that there is a one to one correspondence between anti-Yetter-Drinfeld modules, which serve as coefficients for the Hopf…

We define an abstract regular polytope to be internally self-dual if its self-duality can be realized as one of its symmetries. This property has many interesting implications on the structure of the polytope, which we present here. Then,…

Unlike the Gorenstein projective and injective dimensions, the majority of results on the Gorenstein flat dimension have been established only over Noetherian (or coherent) rings. Naturally, one would like to generalize these results to any…

Let A be a noetherian local commutative ring and let M be a suitable complex of A-modules. This paper proves that M is a dualizing complex for A if and only if the trivial extension A \ltimes M is a Gorenstein Differential Graded Algebra.…

An abelian cover is a finite morphism $X\to Y$ of varieties which is the quotient map for a generically faithful action of a finite abelian group $G$. Abelian covers with $Y$ smooth and $X$ normal were studied in…

We exhibit several transformations of surfaces in R^4. First, one that takes a flat surface and gets a surface with flat normal bundle; then, one that takes a surface with flat normal bundle and gets a flat surface; finally, a one-parameter…

In this paper we treat Grothendieck Duality for noetherian rings via rigid dualizing complexes. In particular, we prove that every ring, essentially finite type over a regular base ring, has a unique rigid dualizing complex. The rigid…

In a pandemic era preprint, Dao showed showed two remarkable properties of Arf rings: under some mild conditions, they admit finitely many indecomposable reflexive modules up to isomorphism and every reflexive module is actually isomorphic…

Mutations occur in multiple algebraic contexts, often enjoying good combinatorial properties. In this paper we study mutations of pure-injective cosilting objects in compactly generated triangulated categories from a topological point of…

In this paper, it is proved, that for varieties with (m-1)-Du Bois singularities, the natural morphism from the Grothendieck dual of the m-th graded Du Bois complex to the Grothendieck dual of its zero-th cohomology sheaf is injective on…

Let R be a commutative ring, and let S be a multiplicative subset of R. In this paper, we introduce and investigate the notion of S-FP-injective modules. Among other results, we show that, under certain conditions, a ring R is S-Noetherian…

We introduce an operation on modules over an $F$-finite ring of characteristic $p$. We call this operation \emph{tight interior}. While it exists more generally, in some cases this operation is equivalent to the Matlis dual of tight…

In this article we realize T-duality as a geometric transform of bundles of abelian group stacks. The transform applies in the algebro-geometric setting as well as the topological setting, and thus makes precise the link between the models…

Let $R$ be a commutative ring and $S \subseteq R$ be a multiplicative subset. We introduce and study the concept of $S$-purity based on the notion of $S$-strongly flat modules. The class of $S$-pure injective modules will be studied. We…

There are several theorems describing the intricate relationship between flatness and associated primes over commutative Noetherian rings. However, associated primes are known to act badly over non-Noetherian rings, so one needs a suitable…

Let R be a commutative noetherian ring. We give criteria for a complex of cotorsion flat R-modules to be minimal, in the sense that every self homotopy equivalence is an isomorphism. To do this, we exploit Enochs' description of the…