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Equivariant resolutions over Veronese rings.
- Source :
-
Journal of the London Mathematical Society . Jan2024, Vol. 109 Issue 1, p1-39. 39p. - Publication Year :
- 2024
-
Abstract
- Working in a polynomial ring S=k[x1,...,xn]$S={\mathbf {k}}[x_1,\ldots ,x_n]$, where k${\mathbf {k}}$ is an arbitrary commutative ring with 1, we consider the d$d$th Veronese subalgebras R=S(d)$R={S^{(d)}}$, as well as natural R$R$‐submodules M=S(⩾r,d)$M={S^{({\geqslant r},{d})}}$ inside S$S$. We develop and use characteristic‐free theory of Schur functors associated to ribbon skew diagrams as a tool to construct simple GLn(k)$GL_n({\mathbf {k}})$‐equivariant minimal free R$R$‐resolutions for the quotient ring k=R/R+${\mathbf {k}}=R/R_+$ and for these modules M$M$. These also lead to elegant descriptions of ToriR(M,M′)$\operatorname{Tor}^R_i(M,M^{\prime})$ for all i$i$ and HomR(M,M′)$\operatorname{Hom}_R(M,M^{\prime})$ for any pair of these modules M,M′$M,M^{\prime}$. [ABSTRACT FROM AUTHOR]
- Subjects :
- *QUOTIENT rings
*K-theory
*POLYNOMIAL rings
*COMMUTATIVE rings
Subjects
Details
- Language :
- English
- ISSN :
- 00246107
- Volume :
- 109
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Journal of the London Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 175054980
- Full Text :
- https://doi.org/10.1112/jlms.12848