Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 0709.3412

Characterization of quasi-coherent modules that are module schemes

Amelia Álvarez Sánchez·Carlos Sancho de Salas·Pedro Sancho de Salas
View original source ↗Read source document ↗Export metadata ↓

Abstract

The R-module functors that are essential for the development of the theory of the linear representations of an affine R-group are the quasi-coherent R-modules and the R-module schemes. The aim of this paper is to study when a quasi-coherent R-module is an R-module scheme. We will prove that it is equivalent to giving a characterization of projective R-modules of finite type.

Explore related subjects

math.AC

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Amelia Álvarez Sánchez, Carlos Sancho de Salas, Pedro Sancho de Salas. 2007-09-28. Characterization of quasi-coherent modules that are module schemes. https://arxiv.org/abs/0709.3412

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Homological subsets of Spec

We recover some data of a module $M$ from the Ext-family $\{Ext^i_R(M,R)\}$. In this regard, we investigate homological subsets of $Spec(R)$, defined by the help of Ext-family. For example, we present a situation for which $\bigcup_{i=0}^\infty Ass(Ext^i_R(M,R))$ is infinite, thereby answering a question of Vasconcelos. We extend Grothendieck's calculation of $dim(Ext^g_R(M,R))$ and present some new situations to calculate $dim(Ext^\ast_R(M,R))$. Also, we compute support and the set of all associated prime ideals of the Ext-family in a serial of nontrivial cases.

math.AC↗
arXiv2026

On Stanley-Reisner Rings with Minimal Betti Numbers

We study simplicial complexes with a given number of vertices whose Stanley-Reisner ring has the minimal sum of Betti numbers. We prove that every full subcomplex of them is homotopy equivalent either to a point or to a sphere. Moreover, we prove that such kind of simplicial complexes coincide with those having minimal Taylor resolutions.

math.AC↗
arXiv2026

Local-Cohen-Macaulay DG-rings with unequal finitistic projective dimensions

For every pair of integers $d,n\geq1$, we construct a commutative noetherian local-Cohen-Macaulay DG-ring $A$ such that $\dim H^0(A)=d$, $\mathrm{amp}(A)=n$, $\mathrm{fpd}(A)=d-n$, and $\mathrm{FPD}(A)=d$. This gives a negative answer to the implication from local-Cohen-Macaulayness to equality of the two finitistic projective dimensions in a question of Bird, Shaul, Sridhar, and Williamson.

math.AC↗