# Regularity of spectral stacks and discreteness of weight-hearts

We study regularity in the context of ring spectra and spectral stacks. Parallel to that, we construct a weight structure on the category of compact quasi-coherent sheaves on spectral quotient stacks of the form $X=[\operatorname{Spec} R/G]$ defined over a field, where $R$ is a connective ${\mathcal{E}_{\infty}}$-$k$-algebra and $G$ is a linearly reductive group acting on $R$... (read more)

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# Categories

• K-THEORY AND HOMOLOGY
• ALGEBRAIC TOPOLOGY