Geller's conjecture on injectivity of for one-dimensional local domains
Geller's conjecture on injectivity of for one-dimensional local domains
Let be a local one-dimensional domain with field of fractions . Geller's conjecture. The ring is regular if and only if the map
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 , but remains unknown in almost all other cases.
Progress summary
Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.
Sources & referencesView supporting material
Primary source
Amalendu Krishna, “On K_2 of 1-dimensional local rings”, arXiv:math/0402190 (2004).
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