OpenAI research collection · 2 manuscripts · Source checked 2026-10-19
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.
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We construct a two-dimensional ramified regular local ring A of mixed characteristic (0,5) for which K_5(A)→ K_5(\mathop{Frac}\nolimits A) has a nonzero kernel. This disproves Gersten's conjecture in its unrestricted integral form.
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We construct a two-dimensional ramified regular local ring A in mixed characteristic (0,5) for which the integral map K_3(A)→ K_3(\mathop{Frac}\nolimits A) has nonzero kernel. This gives a negative answer to the unrestricted integral Gersten conjecture.
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