{"id":"openai-math/An-Integral-Counterexample-to-Gerstens-Conjecture","pdf":"https://github.com/openai/math/blob/main/preprints/An-Integral-Counterexample-to-Gerstens-Conjecture-September-25-2026/An-Integral-Counterexample-to-Gerstens-Conjecture-September-25-2026.pdf","url":"https://github.com/openai/math/tree/main/preprints/An-Integral-Counterexample-to-Gerstens-Conjecture-September-25-2026","tags":["k-theory","commutative-algebra"],"score":0,"title":"An integral counterexample to Gersten's conjecture","domain":"Algebra","family":"209","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.RA","summary":"We construct a two-dimensional ramified regular local ring A of mixed characteristic $`(0,5)`$ for which $`K_5(A)\\to K_5(\\mathop{\\mathrm{Frac}}\\nolimits A)`$ has a nonzero kernel. This disproves Gersten's conjecture in its unrestricted integral form.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-25","reactions":{},"formalized":false,"family_title":"Integral counterexamples to Gersten’s conjecture"}