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Award ID contains: 2200716

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  1. ; (, Journal für die reine und angewandte Mathematik (Crelles Journal))
    Abstract F-signature is an important numeric invariant of singularities in positive characteristic that can be used to detect strong F-regularity.One would like to have a variant that rather detects F-rationality, and there are two theories that aim to fill this gap: F-rational signature of Hochster and Yao and dual F-signature of Sannai.Unfortunately, several important properties of the original F-signature are unknown for these invariants.We find a modification of the Hochster–Yao definition that agrees with Sannai’s dual F-signature and push further the united theory to achieve acompletegeneralization of F-signature. 
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  2. ; ; (, Cambridge University Press)
    Hacon, Christopher; Xu, Chenyang (Ed.)
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  3. ; (, Journal of Algebra)
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  4. ; ; ; ; ; ; (, Publications mathématiques de l'IHÉS)
    Abstract We establish the Minimal Model Program for arithmetic threefolds whose residue characteristics are greater than five. In doing this, we generalize the theory of global $$F$$ F -regularity to mixed characteristic and identify certain stable sections of adjoint line bundles. Finally, by passing to graded rings, we generalize a special case of Fujita’s conjecture to mixed characteristic. 
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