Separable extensions in tensor-triangular geometry and generalized Quillen stratification

Abstract

We study the continuous map induced on spectra by a separable extension of tensor-triangulated categories. We determine the image of this map and relate the cardinality of its fibers to the degree of the extension. We then prove a weak form of descent, "up-to-nilpotence", which allows us to generalize Quillen's Stratification Theorem to equivariant derived categories.

Final revised version, 17 pages, to appear in Ann. Sci. Ecole Norm. Sup. (4). Formula in Thm.3.4(c) corrected

References in corpus (2)

• Stacks of group representations
• Splitting tower and degree of tt-rings

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