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arXiv · 2602.09261

Fibre-Product Stability, Kummer Gluing, and Composita for Universal Koszulity

Marina Palaisti
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Abstract

We study universal Koszulity under algebraic gluing and field composita. For quadratic fibre products, orthogonally split pullbacks reduce to direct sums, while Stanley--Reisner pullbacks arise from graph gluing preserving universal Koszulity under a dominating-clique hypothesis. For composita, Kummer theory and the norm-residue theorem yield a graph criterion from restriction images and degree-two cup-product relations, verified for iterated Laurent-series fields with nonzero mixed symbols. In a nonabelian RAAG family, every finite \(p\)-extension has explicitly determined universally Koszul cohomology, with \[ G_L(p)\cong F_{1+q(d-1)}\times\mathbb Z_p^s.\]

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Marina Palaisti. 2026-02-09. Fibre-Product Stability, Kummer Gluing, and Composita for Universal Koszulity. https://arxiv.org/abs/2602.09261

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