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arXiv · 2606.22193

Computing framed motives

Grigory Garkusha
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Abstract

We develop methods for computing framed motives associated with motivic Thom spectra. Our main tool is a motivic Atiyah--Hirzebruch spectral sequence relating framed motives to framed motivic cohomology. As a consequence, after inverting a finite set of primes, the bigraded homotopy sheaves of motivic Thom spectra are computed in terms of framed motivic cohomology. We further analyze the symmetric-group actions inherent in framed correspondences and introduce a theory of torsion framed motivic cohomology that yields new computational descriptions of framed motivic cohomology groups. These constructions lead to a category of permutation-free framed correspondences from which we reconstruct rational stable motivic homotopy theory.

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Grigory Garkusha. 2026-06-20. Computing framed motives. https://arxiv.org/abs/2606.22193

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