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Creators/Authors contains: "Bragg, Daniel"

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  1. (, Bulletin of the London Mathematical Society)
    We show that a Fourier–Mukai equivalence between smooth projective varieties of characteristic that commutes with either pushforward or pullback along Frobenius is a composition of shifts, isomorphisms, and tensor products with invertible sheaves whose th tensor power is trivial. 
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    Free, publicly-accessible full text available November 1, 2025
  2. ; ; (, Mathematische Annalen)
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  3. ; (, Algebra and number theory)
    Accepted Manuscript Full Text Available
  4. ; (, Algebraic Geometry)
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  5. ; (, Compositio Mathematica)
    We describe a method to show that certain elliptic surfaces do not admit purely inseparable multisections (equivalently, that genus 1 curves over function fields admit no points over the perfect closure of the base field) and use it to show that any non-Jacobian elliptic structure on a very general supersingular K3 surface has no purely inseparable multisections. We also describe specific examples of genus 1 fibrations on supersingular K3 surfaces without purely inseparable multisections. 
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  6. (, International Mathematics Research Notices)
    Abstract Deligne [9] showed that every K3 surface over an algebraically closed field of positive characteristic admits a lift to characteristic 0. We show the same is true for a twisted K3 surface. To do this, we study the versal deformation spaces of twisted K3 surfaces, which are particularly interesting when the characteristic divides the order of the Brauer class. We also give an algebraic construction of certain moduli spaces of twisted K3 surfaces over $${\operatorname {Spec}}\ \textbf {Z}$$ and apply our deformation theory to study their geometry. As an application of our results, we show that every derived equivalence between twisted K3 surfaces in positive characteristic is orientation preserving. 
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