The ideal-adic semi-continuity conjecture for minimal log discrepancies
Let be a klt variety, let be a closed point, and let denote the maximal ideal corresponding to . Ideal-adic semi-continuity conjecture. For every given , there exists such that, for any ideal sheaves and on satisfying
one has
This conjecture asserts that the minimal log discrepancy at is determined by a sufficiently high ideal-adic jet. The source attributes it to Mustață and Nakamura and presents it in a paper that gives a counterexample to a related conjectural property; the supplied text does not state that this conjecture itself is resolved.
References
Primary source
Yusuke Nakamura and Kohsuke Shibata, “A counterexample to the PIA conjecture for minimal log discrepancies”, arXiv:2404.06164 (2026).
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