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Creators/Authors contains: "Satriano, Matthew"

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  1. ; (, SIAM Journal on Applied Algebra and Geometry)
    Draisma, Jan (Ed.)
    Abstract.We study the third moment for functions on arbitrary compact Lie groups. 
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  2. ; ; (, Forum of Mathematics, Sigma)
    Abstract We define a notion of height for rational points with respect to a vector bundle on a proper algebraic stack with finite diagonal over a global field, which generalizes the usual notion for rational points on projective varieties. We explain how to compute this height for various stacks of interest (for instance: classifying stacks of finite groups, symmetric products of varieties, moduli stacks of abelian varieties, weighted projective spaces). In many cases, our uniform definition reproduces ways already in use for measuring the complexity of rational points, while in others it is something new. Finally, we formulate a conjecture about the number of rational points of bounded height (in our sense) on a stack $$\mathcal {X}$$ , which specializes to the Batyrev–Manin conjecture when $$\mathcal {X}$$ is a scheme and to Malle’s conjecture when $$\mathcal {X}$$ is the classifying stack of a finite group. 
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  3. ; ; ; ; (, ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE)
    null (Ed.)
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  4. ; (, International Mathematics Research Notices)
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  5. ; (, Ergodic Theory and Dynamical Systems)
    Let be a dominant rational self-map of a smooth projective variety defined over $$\overline{\mathbb{Q}}$$ . For each point $$P\in X(\overline{\mathbb{Q}})$$ whose forward $$f$$ -orbit is well defined, Silverman introduced the arithmetic degree $$\unicode[STIX]{x1D6FC}_{f}(P)$$ , which measures the growth rate of the heights of the points $$f^{n}(P)$$ . Kawaguchi and Silverman conjectured that $$\unicode[STIX]{x1D6FC}_{f}(P)$$ is well defined and that, as $$P$$ varies, the set of values obtained by $$\unicode[STIX]{x1D6FC}_{f}(P)$$ is finite. Based on constructions by Bedford and Kim and by McMullen, we give a counterexample to this conjecture when $$X=\mathbb{P}^{4}$$ . 
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  6. ; (, International Mathematics Research Notices)
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