LAUSR.org creates dashboard-style pages of related content for over 1.5 million academic articles. Sign Up to like articles & get recommendations!

The prime spectra of relative stable module categories

Photo from academic.microsoft.com

For a finite group $G$ and an arbitrary commutative ring $R$, Brou\'e has placed a Frobenius exact structure on the category of finitely generated $RG$-modules by taking the exact sequences… Click to show full abstract

For a finite group $G$ and an arbitrary commutative ring $R$, Brou\'e has placed a Frobenius exact structure on the category of finitely generated $RG$-modules by taking the exact sequences to be those that split upon restriction to the trivial subgroup. The corresponding stable category is then tensor triangulated. In this paper we examine the case $R=S/t^n$, where $S$ is a discrete valuation ring having uniformising parameter $t$. We prove that the prime ideal spectrum (in the sense of Balmer) of this `relative' version of the stable module category of $RG$ is a disjoint union of $n$ copies of that for $kG$, where $k$ is the residue field of $S$.

Keywords: prime spectra; module; relative stable; stable module; spectra relative; module categories

Journal Title: Transactions of the American Mathematical Society
Year Published: 2018

Link to full text (if available)


Share on Social Media:                               Sign Up to like & get
recommendations!

Related content

More Information              News              Social Media              Video              Recommended



                Click one of the above tabs to view related content.