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Creators/Authors contains: "Tayou, Salim"

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  1. ; ; (, International Mathematics Research Notices)
    Given a smooth quasi-projective complex algebraic variety $$\mathcal{S}$$, we prove that there are only finitely many Hodge-generic non-isotrivial families of smooth projective hypersurfaces over $$\mathcal{S}$$ of degree $$d$$ in $$\mathbb{P}_{\mathbb C}^{n+1}$$. We prove that the finiteness is uniform in $$\mathcal{S}$$ and give examples where the result is sharp. We also prove similar results for certain complete intersections in $$\mathbb{P}_{\mathbb C}^{n+1}$$ of higher codimension and more generally for algebraic varieties whose moduli space admits a period map that satisfies the infinitesimal Torelli theorem. 
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    Free, publicly-accessible full text available August 1, 2026
  2. (, Algebra & Number Theory)
    Free, publicly-accessible full text available January 1, 2026
  3. ; (, Journal of the London Mathematical Society)
    Abstract Given a Brauer class on a K3 surface defined over a number field, we prove that there exists infinitely many reductions where the Brauer class vanishes, under certain technical hypotheses, answering a question of Frei–Hassett–Várilly‐Alvarado. 
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    Free, publicly-accessible full text available January 1, 2026
  4. ; ; ; (, Forum of Mathematics, Pi)
    Abstract Given a K3 surface X over a number field K with potentially good reduction everywhere, we prove that the set of primes of K where the geometric Picard rank jumps is infinite. As a corollary, we prove that either $$X_{\overline {K}}$$ has infinitely many rational curves or X has infinitely many unirational specialisations. Our result on Picard ranks is a special case of more general results on exceptional classes for K3 type motives associated to GSpin Shimura varieties. These general results have several other applications. For instance, we prove that an abelian surface over a number field K with potentially good reduction everywhere is isogenous to a product of elliptic curves modulo infinitely many primes of K . 
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