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math.AG2026
Quadratic Spaces and Orthogonal Groups over semilocal Rings
Philippe Gille, Erhard Neher
We prove Springer's Odd Degree Theorem for quadratic forms over LG rings, and Scharlau's and Knebusch's norm principles for quadratic forms over semilocal rings. We present applica…
math.AG2026
Loop torsors and Abhyankar's lemma
Philippe Gille
We define the notion of loop torsors under certain group schemes defined over the localization of a regular henselian ring A at a strict normal crossing divisor D. We provide a Gal…