Geller's conjecture on injectivity of K2K_2 for one-dimensional local domains

At least 21 years old · documented by

Let AA be a local one-dimensional domain with field of fractions FF. Geller's conjecture. The ring AA is regular if and only if the map

K2(A)⟶K2(F)K_2(A)\longrightarrow K_2(F)

is injective.

The conjecture gives a criterion for regularity in terms of the injectivity of the map from the second algebraic K-group of a singular or regular local ring to that of its fraction field. It was verified in several cases, including noetherian equicharacteristic characteristic-zero rings that are seminormal with finite normalisation and cuspidal rings of the form K[t2,t3]K[t^2,t^3], but remains unknown in almost all other cases.

References

Primary source

Amalendu Krishna, “On K_2 of 1-dimensional local rings”, arXiv:math/0402190 (2004).

Progress summary

Never refreshed

Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.

Solutions 0

No solutions have been posted yet.