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Creators/Authors contains: "Polstra, Thomas"

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  1. ; ; (, Cambridge University Press)
    Hacon, Christopher; Xu, Chenyang (Ed.)
    Free, publicly-accessible full text available January 2, 2026
  2. ; ; (, Advances in Mathematics)
    Full Text Available 
  3. ; (, Proceedings of the American Mathematical Society)
    Suppose R R is a F F -finite and F F -pure Q \mathbb {Q} -Gorenstein local ring of prime characteristic p > 0 p>0 . We show that an ideal I ⊆<#comment/> R I\subseteq R is uniformly compatible ideal (with all p −<#comment/> e p^{-e} -linear maps) if and only if exists a module finite ring map R →<#comment/> S R\to S such that the ideal I I is the sum of images of all R R -linear maps S →<#comment/> R S\to R . In other words, the set of uniformly compatible ideals is exactly the set of trace ideals of finite ring maps. 
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  4. ; (, Michigan Mathematical Journal)
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  5. ; (, Nagoya Mathematical Journal)
    We establish the continuity of Hilbert–Kunz multiplicity and F-signature as functions from a Cohen–Macaulay local ring $$(R,\mathfrak{m},k)$$ of prime characteristic to the real numbers at reduced parameter elements with respect to the $$\mathfrak{m}$$ -adic topology. 
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  6. ; ; ; ; (, Journal of Singularities)
    null (Ed.)
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  7. ; (, Journal of Algebra)
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  8. ; ; ; (, Forum of Mathematics, Sigma)
    We study $$F$$ -signature under proper birational morphisms $$\unicode[STIX]{x1D70B}:Y\rightarrow X$$ , showing that $$F$$ -signature strictly increases for small morphisms or if $$K_{Y}\leqslant \unicode[STIX]{x1D70B}^{\ast }K_{X}$$ . In certain cases, we can even show that the $$F$$ -signature of $$Y$$ is at least twice as that of  $$X$$ . We also provide examples of $$F$$ -signature dropping and Hilbert–Kunz multiplicity increasing under birational maps without these hypotheses. 
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