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The Quarterly Journal of Mathematics Advance Access published online on December 19, 2008
The Quarterly Journal of Mathematics, doi:10.1093/qmath/han032
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© The author 2008. Published by Oxford University Press. All rights reserved. For permissions, please email: journals.permissions@oxfordjournals.org

RELATIVE SUPPORT VARIETIES

Petter Andreas Bergh{dagger} and Øyvind Solberg {ddagger}

Institutt for matematiske fag, NTNU, N-7491 Trondheim, Norway

{dagger} Corresponding author. E-mail: bergh{at}math.ntnu.no

Received 25 April 2008; revised 23 August 2008
  Abstract

We define relative support varieties with respect to some fixed module over a finite-dimensional algebra. These varieties share many of the standard properties of classical support varieties. Moreover, when introducing finite-generation conditions on cohomology, we show that relative support varieties contain homological information on the modules involved. As an application, we provide a new criterion for a selfinjective algebra to be of wild representation type.

{ddagger} E-mail: oyvinso{at}math.ntnu.no


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