Homogeneous spaces in tensor categories

2025/05/07 by Coulembier, Kevin, Sherman, Alexander · 1 citation
#Algebraic Geometry (math.AG) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2505.04848

Abstract

Let \mathscrC be a symmetric tensor category of moderate growth, and let H\subseteqG be algebraic groups in \mathscrC. We prove that the homogeneous space G/H exists and is of finite type when \mathscrC satisfies (GR) and (MN1-2), which are conjecturally equivalent to incompressibility. A key tool is the introduction of a Frobenius kernel of an group scheme. We further show that while G₀/H₀ and (G/H)₀ need not be the same, they are close enough, so that G/H is quasi-affine/affine/proper if and only if G₀/H₀ is.

Citations

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Cited by

• Group schemes and their Lie algebras over a symmetric tensor category

Related

• Symmetric tensor categories in characteristic 2
• Commutative algebra in tensor categories
• Quasi-Frobenius algebras in finite tensor categories
• Group schemes and their Lie algebras over a symmetric tensor category
• Tensor spaces and the geometry of polynomial representations