Related papers: Valuation rings are derived splinters
We prove a desingularization theorem for the quasi-smooth derived scheme, in the sense of Hekking. We also propose the conjecture that the K-theoretic integration of the virtual fundamental class of a quasi-smooth derived scheme could be…
The classification of gradings by abelian groups on finite direct sums of simple finite-dimensional nonassociative algebras over an algebraically closed field is reduced, by means of the use of loop algebras, to the corresponding problem…
Hall's binomial rings, rings with binomial coefficients, are given an axiomatisation and proved identical to the numerical rings studied by Ekedahl. The Binomial Transfer Principle is established, enabling combinatorial proofs of…
We classify dp-minimal integral domains, building off the existing classification of dp-minimal fields and dp-minimal valuation rings. We show that if R is a dp-minimal integral domain, then R is a field or a valuation ring or arises from…
We prove basic facts about reflexivity in derived categories over noetherian schemes; and about related notions such as semidualizing complexes, invertible complexes, and Gorenstein-perfect maps. Also, we study a notion of rigidity with…
Let $K$ be the field of Laurent series with complex coefficients, let $\mathcal{R}$ be the inverse limit of the standard-graded polynomial rings $K[x_1, \ldots, x_n]$, and let $\mathcal{R}^{\flat}$ be the subring of $\mathcal{R}$ consisting…
In this study we consider domains that are composed of an infinite sequence of self-similar rings and corresponding finite element spaces over those domains. The rings are parameterized using piecewise polynomial or tensor-product B-spline…
This is a continuation of a previous paper by the same authors. In the former paper, it was proved that in order to obtain local uniformization for valuations centered on local domains, it is enough to prove it for rank one valuations. In…
The geometric and algebraic theory of valuations on cones is applied to understand identities involving summing certain rational functions over the set of linear extensions of a poset.
Measure and integral are two closely related, but distinct objects of study. Nonetheless, they are both real-valued lattice valuations: order preserving real-valued functions $\phi$ on a lattice $L$ which are modular, i.e.,…
In this paper, we explain how some basic facts about valuation can help clarify many questions about divisibility in integral domains.
A graded-division algebra is an algebra graded by a group such that all nonzero homogeneous elements are invertible. This includes division algebras equipped with an arbitrary group grading (including the trivial grading). We show that a…
We prove that the $\infty$-category of surjections of animated rings is projectively generated, introduce and study the notion of animated PD-pairs - surjections of animated rings with a "derived" PD-structure. This allows us to generalize…
We prove that the stable endomorphism rings of rigid objects in a suitable Frobenius category have only finitely many basic algebras in their derived equivalence class and that these are precisely the stable endomorphism rings of objects…
In a k-linear triangulated category (where k is a field) we show that the existence of Auslander-Reiten triangles implies that objects are determined, up to shift, by knowing dimensions of homomorphisms between them. In most cases the…
This paper proposes new derivations of three well-known sorting algorithms, in their functional formulation. The approach we use is based on three main ingredients: first, the algorithms are derived from a simpler algorithm, i.e. the…
In this survey, we describe two different approaches to constructing affine schemes for commutative semirings: one based on prime ideals, and another based on prime kernels (also called subtractive ideals). We then explain how these two…
We introduce a notion of generalized homogeneous derivations on graded rings as a natural extension of the homogeneous derivations defined by Kanunnikov. We then define gr-generalized derivations, which preserve the degrees of homogeneous…
This paper shows a finiteness property of a divisorial valuation in terms of arcs. First we show that every divisorial valuation over an algebraic variety corresponds to an irreducible closed subset of the arc space. Then we define the…
A study of the relation between a noetherian local domain with a given valuation and its associated graded ring with respect to the valuation, which in some cases is an esentially toric variety, possibly of infinite embedding dimension, but…