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Creators/Authors contains: "Alper, Jarod"

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  1. ; ; ; (, Forum of Mathematics, Sigma)
    We give a variant of Artin algebraization along closed subschemes and closed substacks. Our main application is the existence of étale, smooth, or syntomic neighborhoods of closed subschemes and closed substacks. In particular, we prove local structure theorems for stacks and their derived counterparts and the existence of henselizations along linearly fundamental closed substacks. These results establish the existence of Ferrand pushouts, which answers positively a question of Temkin-Tyomkin. 
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    Accepted Manuscript Full Text Available
  2. ; ; ; (, Inventiones mathematicae)
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  3. ; ; ; (, Inventiones mathematicae)
    null (Ed.)
    We prove that K-polystable log Fano pairs have reductive automorphism groups. In fact, we deduce this statement by establishing more general results concerning the S-completeness and Θ-reductivity of the moduli of K-semistable log Fano pairs. Assuming the conjecture that K-semistability is an open condition, we prove that the Artin stack parametrizing K-semistable Fano varieties admits a separated good moduli space. 
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    Accepted Manuscript Full Text Available