Local duality for representations of finite group schemes

Abstract

A duality theorem for the stable module category of representations of a finite group scheme is proved. One of its consequences is an analogue of Serre duality, and the existence of Auslander-Reiten triangles for the $\mathfrak{p}$-local and $\mathfrak{p}$-torsion subcategories of the stable category, for each homogeneous prime ideal $\mathfrak{p}$ in the cohomology ring of the group scheme.

24 pages. This version corrects a mistake in the statement of Theorem 3.1; see also Theorem 1.4, and Examples 3.6 and 3.7. References have been updated

References in corpus (2)

• Local duality for structured ring spectra
• Colocalising subcategories of modules over finite group schemes

Cited by in corpus (1)

• Definable functors between triangulated categories