{"id":"palomar/PALOMAR-2026-10-21-000024","url":"https://github.com/itpplasma/symplectic-stafford-formal/tree/0e55a8059cc923ef39d6ddb66c5b6f6a2682b46b","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-10-21-000024-v1.json","repo":"https://github.com/itpplasma/symplectic-stafford-formal","tags":["math.RA","math.AG","msc:16S32","msc:16S38","ring-theory","algebra","stable-range","lean"],"score":0,"title":"Symplectic Stafford: the affine same-divisor theorem","trust":"high","domain":"math.RA","source":"palomar","authors":["Christopher Albert"],"reviews":0,"subject":"math.RA","summary":"Let k be a field of characteristic zero and U a simple, infinite-dimensional k-algebra with an exhaustive nonnegative multiplicative filtration by finite-dimensional k-subspaces. Suppose F_0 U = k and the associated graded algebra is a commutative affine domain of finite Krull dimension. Then for every nonzero d, a in U and every B in U there exist H, R, S in U such that 1 = dR + (B + Ha)dS. The Lean 4 development proves this theorem, its left-handed form, and module generation, stable range and cancellation results for U.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-10-21","reactions":{},"formalized":true}