Related papers: Graded perfectoid rings
This is release 7.5 of our project, aiming to provide a complete treatment of the foundations of almost ring theory, following and extending Faltings's method of "almost etale extensions". The central result is the "almost purity theorem",…
Let $R$ be a graded ring. We introduce a class of graded $R$-modules called Gr\"obner-coherent modules. Roughly, these are graded $R$-modules that are coherent as ungraded modules because they admit an adequate theory of Gr\"obner bases.…
We investigate the interplay of crystal bases and completions in the sense of Enright on certain nonintegrable representations of quantum groups. We define completions of crystal bases, show that this notion of completion is compatible with…
We extend Faltings's "almost purity theorem" on finite etale extensions of perfectoid algebras (as generalized by Scholze and Kedlaya-Liu) to the ramified case, without restriction on the discriminant. The key point is a perfectoid version…
We present a scheme in which we investigate the two-slit experiment and the the principle of complementarity.
We investigate equivalences between the categories of perfects complexes of the quotients of two smooth projective schemes by the action of a finite group. As a result we give a necessary and sufficient condition for an equivalence between…
Stably supported quantales generalize pseudogroups and provide an algebraic context in which to study the correspondences between inverse semigroups and \'etale groupoids. Here we study a further generalization where a non-unital version of…
We establish a generalization of the Briancon-Skoda theorem about integral closures of ideals for graded systems of ideals satisfying a certain geometric condition.
In this paper, we will consider derived equivalences for differential graded endomorphism algebras by Keller's approaches. First we construct derived equivalences of differential graded algebras which are endomorphism algebras of the…
We introduce a graded homology theory for graded \'etale groupoids. For $\mathbb Z$-graded groupoids, we establish an exact sequence relating the graded zeroth-homology to non-graded one. Specialising to the arbitrary graph groupoids, we…
A relationship between curved differential algebras and corings is established and explored. In particular it is shown that the category of semi-free curved differential graded algebras is equivalent to the category of corings with…
We describe the graded isomorphisms of rings of endomorphisms of graded flags over graded division algebras. As a consequence describe the isomorphism classes of upper block triangular matrix algebras (over an algebraically closed field of…
We prove that a unital shift equivalence induces a graded isomorphism of Leavitt path algebras when the shift equivalence satisfies an alignment condition. This yields another step towards confirming the Graded Classification Conjecture.…
In the first part, we revisit the theory of Drinfeld modular curves and $\pi$-adic Drinfeld modular forms for GL(2) from the perfectoid point of view. In the second part, we review open problems for families of Drinfeld modular forms for…
We classify crossed product gradings for arbitrary groups and fields up to several equivalence relations in terms of group actions and their orbits.
Characteristic properties of corings with a grouplike element are analysed. Associated differential graded rings are studied. A correspondence between categories of comodules and flat connections is established. A generalisation of the…
In this article, we introduce the concepts of graded $s$-prime submodules which is a generalization of graded prime submodules. We study the behavior of this notion with respect to graded homomorphisms, localization of graded modules,…
Due to their elegant and simple nature, unitary Cayley graphs have been an active research topic in the literature. These graphs are naturally connected to several branches of mathematics, including number theory, finite algebra,…
We continue the study on sheaves of rings on finite posets. We present examples where the ring of global sections coincide with toric faces rings, quotients of a polynomial ring by a monomial ideal and algebras with straightening laws. We…
We develop a Van der Waerden type theorem in an axiomatic setting of graded lattices and show that this axiomatic formulation can be applied to various lattices, for instance the set partition and the Boolean lattices. We derive the…