In countably-normed spaces of functions on a torus that are smooth in one or both variables, we study Toeplitz operators with symbols ensure the bounded these spaces. To bisingular type summable and Ho¨lder functions, method partial regularization was used. Using this method, obtain construction regularizer condition for operator to be Noetherian space variables. Despite fact set space, unlike ...

We consider the Noetherian properties of the ring of differential operators of an affine semigroup algebra. First we show that it is always right Noetherian. Next we give a condition, based on the data of the difference between the semigroup and its scored closure, for the ring of differential operators being anti-isomorphic to another ring of differential operators. Using this, we prove that t...

Let X be an Artin stack (always assumed to have quasi-compact and separated diagonal over SpecZ; cf. [2, §1.3]). A coarse moduli space for X is a map π : X → X to an algebraic space such that (i) π is initial among maps from X to algebraic spaces (note that the category of maps from X to an algebraic space is discrete), and (ii) for every algebraically closed field k the map [X (k)]→ X(k) is bi...

Let S be a Noetherian scheme, φ : X → Y a surjective S-morphism of S-schemes, with X of finite type over S. We discuss what makes Y of finite type. First, we prove that if S is excellent, Y is reduced, and φ is universally open, then Y is of finite type. We apply this to understand Fogarty’s theorem in “Geometric quotients are algebraic schemes, Adv. Math. 48 (1983), 166–171” for the special ca...

In this paper we introduce a new class of modules which is closely related to the class of Noetherian modules. Let $R$ be a commutative ring with identity and let $M$ be an $R$-module such that $Nil(M)$ is a divided prime submodule of $M$. $M$ is called a Nonnil-Noetherian $R$-module if every nonnil submodule of $M$ is finitely generated. We prove that many of the properties of Noetherian modul...

Abstract We define the notion of a specialization morphism from locally noetherian analytic adic space to scheme. This captures (classical) associated with formal There is well-behaved theory compactifications and it turns out that classical proper in this setup. As an application, we show nearby cycles functor commutes lower shriek great generality.

Let (R,m) be a commutative Noetherian local ring with m = (0). We give a condition for R to have a non-free module of G-dimension zero. We shall also construct a family of non-isomorphic indecomposable modules of G-dimension zero with parameters in an open subset of projective space. We shall finally show that the subcategory consisting of modules of G-dimension zero over R is not necessarily a...

We develop some of the foundations of affinoid pre-adic spaces without Noetherian or finiteness hypotheses. We give explicit examples of non-adic affinoid pre-adic spaces, and also a new condition ensuring that the structure presheaf on Spa(R,R) is a sheaf. This condition can be used to give a new proof that the spectrum of a perfectoid algebra is an adic space.

We determine the relationship between the cardinality of a Noetherian integral domain and the cardinality of a residue field. One consequence of the main result is that it is provable in ZFC that there is a Noetherian domain of cardinality א1 with a finite residue field, but the statement “There is a Noetherian domain of cardinality א2 with a finite residue field” is equivalent to the negation ...

A non-commutative space X is a Grothendieck category ModX. We say X is integral if there is an indecomposable injective X-module EX such that its endomorphism ring is a division ring and every X-module is a subquotient of a direct sum of copies of EX . A noetherian scheme is integral in this sense if and only if it is integral in the usual sense. We show that several classes of non-commutative ...