Disproves unrestricted integral Gersten injectivity in degrees 3 and 5. Two explicit two-dimensional ramified regular local rings of mixed characteristic (0,5) have nonzero integral K-theory classes that vanish over their fraction fields.
Manuscripts (2)
An integral counterexample to Gersten's conjecture
September 25, 2026 · source · cite as \cite{OAI:An-Integral-Counterexample-to-Gerstens-Conjecture-September-25-2026}
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.
An integral degree-three Gersten counterexample
September 26, 2026 · source · cite as \cite{OAI:An-Integral-Degree-Three-Gersten-Counterexample-September-26-2026}
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.
Result 209 · Algebra. Imported from openai/math, a collection of manuscripts produced by an OpenAI model; results are at different stages of verification. Discussion below is by Lemma members.
Source: https://github.com/openai/math/blob/main/CONTENTS.md