A Noetherian ring R is a splinter if and only if every equidimensional surjective morphism Spec(S) to Spec(R) makes R to S pure.
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The authors establish the Carvajal-Rojas-Schwede-Tucker conjecture on positive limiting F-signature for two specific classes of complex KLT singularities using inductive arguments and toric degenerations inspired by K-stability.
Quasi-F^e-splitting for all e implies numerically log canonical for numerically Q-Gorenstein normal singularities, with converse in dim 2 when p does not divide the Gorenstein index, plus a classification of 2D quasi-F-split cases.
Under a codimension assumption on the singular locus, isomorphism of the m-th differential sheaf implies isomorphisms for all lower i on complex hypersurfaces, with a positive characteristic analogue discussed.
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Equidimensional morphisms onto splinters are pure
A Noetherian ring R is a splinter if and only if every equidimensional surjective morphism Spec(S) to Spec(R) makes R to S pure.