Integral counterexamples to Gersten’s conjecture

What OpenAI claims

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.

Papers (2)

1. An integral counterexample to Gersten's conjecture

   25 September 2026 · Preprint, not peer reviewed · PDF

   We construct a two-dimensional ramified regular local ring A of mixed characteristic (0,5) for which K₅(A) → K₅(Frac A) has a nonzero kernel. This disproves Gersten's conjecture in its unrestricted integral form.

2. An integral degree-three Gersten counterexample

   26 September 2026 · Preprint, not peer reviewed · PDF

   We construct a two-dimensional ramified regular local ring A in mixed characteristic (0,5) for which the integral map K₃(A) → K₃(Frac A) has nonzero kernel. This gives a negative answer to the unrestricted integral Gersten conjecture.

Status

Preprint. The papers have not been independently reviewed. Treat the result as OpenAI's claim until other mathematicians have checked it. If a video exists, it illustrates the statement; it is not the proof.