arXiv math/05073042005-07-15math.ACmath.AG

Pure subrings of regular rings are pseudo-rational

Hans Schoutens

发表信息：: Trans. Amer. Math. Soc. 360 (2008), 609-627

英文摘要：

We prove a generalization of the Hochster-Roberts-Boutot-Kawamata Theorem conjectured by Aschenbrenner and the author: let $R\to S$ be a pure homomorphism of equicharacteristic zero Noetherian local rings. If $S$ is regular, then $R$ is pseudo-rational, and if $R$ is moreover $\mathbb Q$-Gorenstein, then it pseudo-log-terminal.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

阅读原文

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

本文内容

英文摘要相关论文

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

继续探索

相关论文

Veronese subrings and tight closure

We determine when graded rings have F-rational or F-regular Veronese subrings, and develop techniques of constructing F-rational rings which are not F-regular.

2002-10-07math.AC

The absolutely Koszul property of Veronese subrings and Segre products

Absolutely Koszul algebras are a class of rings over which any finite graded module has a rational Poincaré series. We provide a criterion to detect non-absolutely Koszul rings. Combining the criterion with machine computations, we identify large families of Veronese subrings and Segre products of polynomial rings which are not absolutely Koszul. In particular, we classify completely the absolutely Koszul algebras among Segre products of polynomial rings, at least in characteristic $0$.

2017-04-25math.ACmath.RA

Symmetric and Pseudo-Symmetric Numerical Semigroups via Young Diagrams and Their Semigroup Rings

This paper studies Young diagrams of symmetric and pseudo-symmetric numerical semigroups and describes new operations on Young diagrams as well as numerical semigroups. These provide new decompositions of symmetric and pseudo-symmetric semigroups into an over semigroup and its dual. It is also given exactly for what kind of numerical semigroup $S$, the semigroup ring $\Bbbk[\![S]\!]$ has at least one Gorenstein subring and has at least one Kunz subring.

2020-11-17math.ACmath.COmath.GR

Permutohedral spaces and the Cox ring of the moduli space of stable pointed rational curves

We study the Cox ring of the moduli space of stable pointed rational curves, \M_{0,n}, via the closely related permutohedral (or Losev-Manin) spaces. Our main result establishes \binom{n}{2} polynomial subrings of the Cox ring, thus giving collections of boundary variables that intersect the ideal of relations trivially. As applications, we give a combinatorial way to partially solve the Riemann-Roch problem for \M_{0,n}, and we show that all relations in degrees of Cox(\M_{0,6}) arising from certain pull-backs from projective spaces are generated by the Plucker relations.

2011-05-25math.ACmath.AG

The F-signature of an affine semigroup ring

We prove that the F-signature of an affine semigroup ring of positive characteristic is always a rational number, and describe a method for computing this number. We use this method to determine the F-signature of Segre products of polynomial rings, and of Veronese subrings of polynomial rings. Our technique involves expressing the F-signature of an affine semigroup ring as the difference of the Hilbert-Kunz multiplicities of two monomial ideals, and then using Watanabe's result that these Hilbert-Kunz multiplicities are rational numbers.

2004-09-09math.AC

Almost free splitters

Let R be a subring of the rationals. We want to investigate self splitting R-modules G that is Ext_R(G,G)=0 holds. For simplicity we will call such modules splitters. Our investigation continues math.LO/9910159. In math.LO/9910159, we answered an open problem by constructing a large class of splitters. Classical splitters are free modules and torsion-free, algebraically compact ones. In math.LO/9910159 we concentrated on splitters which are larger then the continuum and such that countable submodules are not necessarily free. The `opposite' case of aleph_1-free splitters of cardinality less or…

1999-10-28math.ACmath.LOmath.RA

更多相关论文收起更多论文

有理函数Prüfer域上矩阵的幂等分解

Idempotent factorization of matrices over a Prüfer domain of rational functions

本文针对Prüfer非Bézout域的公开问题，研究了有理函数极小Dress环（一种Prüfer域上2×2奇异矩阵的幂等分解问题，给出了保证其可分解为幂等矩阵乘积的若干条件。

2021-02-02math.ACmath.RA

Decidability of the theory of addition and the Frobenius map in rings of rational functions

We prove model completeness for the theory of addition and the Frobenius map for certain subrings of rational functions in positive characteristic. More precisely: Let $p$ be a prime number, $\mathbb{F}_{p}$ the prime field with $p$ elements, $F$ a field algebraic over $\mathbb{F}_p$ and $z$ a variable. We show that the structures of rings $R$, which are generated over $F[z]$ by adjoining a finite set of inverses of irreducible polynomials of $F[z]$ (e.g., $R=\mathbb{F}_p[z, \frac{1}{z}]$), with addition, the Frobenius map $x\mapsto x^p$ and the predicate '$\in F$' - together with function sym…

2021-07-23math.ACmath.LOmath.NT

全局化伪赋值域上的整值有理函数

Integer-valued rational functions over globalized pseudovaluation domains

本文研究整值有理函数环成为全局化伪赋值域的条件，证明了伪奇异GPVD上该环仍为GPVD，并完整刻画了非赋值域的伪赋值域情形。

2024-05-01math.AC

有理Witt向量与相伴层

Rational Witt vectors and associated sheaves

本文研究有理Witt向量$W_{\mathrm{rat}}$的层化，证明其与有限平坦拓扑下的相伴层同构，并给出Almkvist定理的新几何解释。

2025-08-07math.ACmath.AG

Extending valuations to the field of rational functions using pseudo-monotone sequences

Let $V$ be a valuation domain with quotient field $K$. We show how to describe all extensions of $V$ to $K(X)$ when the $V$-adic completion $\widehat{K}$ is algebraically closed, generalizing a similar result obtained by Ostrowski in the case of one-dimensional valuation domains. This is accomplished by realizing such extensions by means of pseudo-monotone sequences, a generalization of pseudo-convergent sequences introduced by Chabert. We also show that the valuation rings associated to pseudo-convergent and pseudo-divergent sequences (two classes of pseudo-monotone sequences) roughly corresp…

2021-05-28math.ACmath.RA

Prüfer intersection of valuation domains of a field of rational functions

Let $V$ be a rank one valuation domain with quotient field $K$. We characterize the subsets $S$ of $V$ for which the ring of integer-valued polynomials ${\rm Int}(S,V)=\{f\in K[X] \mid f(S)\subseteq V\}$ is a Prüfer domain. The characterization is obtained by means of the notion of pseudo-monotone sequence and pseudo-limit in the sense of Chabert, which generalize the classical notions of pseudo-convergent sequence and pseudo-limit by Ostrowski and Kaplansky, respectively. We show that ${\rm Int}(S,V)$ is Prüfer if and only if no element of the algebraic closure $\overline{K}$ of $K$ is a pseu…

2018-05-17math.ACmath.RA