Infinite dimensional modules for Frobenius kernels

✍ Scribed by Julia Pevtsova

• Publisher: Elsevier Science
• Year: 2002
• Tongue: English
• Weight: 234 KB
• Volume: 173
• Category: Article
• ISSN: 0022-4049
• DOI: 10.1016/s0022-4049(01)00168-2

✦ Synopsis

We prove that the projectivity of an arbitrary (possibly inÿnite dimensional) module for a Frobenius kernel can be detected by restrictions to one-parameter subgroups. Building upon this result, we introduce the support cone of such a module, extending the construction of support variety for a ÿnite dimensional module, and show that such support cones satisfy most of the familiar properties of support varieties. We also verify that our representation-theoretic deÿnition of support cones admits an interpretation in terms of Rickard idempotent modules associated to thick subcategories of the stable category of ÿnite dimensional modules.