{"id":"openai-math/An-Integral-Degree-Three-Gersten-Counterexample","pdf":"https://github.com/openai/math/blob/main/preprints/An-Integral-Degree-Three-Gersten-Counterexample-September-26-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/An-Integral-Degree-Three-Gersten-Counterexample-September-26-2026","tags":["k-theory","commutative-algebra"],"score":0,"title":"An integral degree-three Gersten counterexample","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 in mixed characteristic $`(0,5)`$ for which the integral map $`K_3(A)\\to K_3(\\mathop{\\mathrm{Frac}}\\nolimits A)`$ has nonzero kernel. This gives a negative answer to the unrestricted integral Gersten conjecture.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-26","reactions":{},"formalized":false,"family_title":"Integral counterexamples to Gersten’s conjecture"}