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Creators/Authors contains: "Katz, Nicholas M."

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  1. ; ; (, European Journal of Mathematics)
    Abstract We study certain one-parameter families of exponential sums of Airy–Laurent type. Their general theory was developed in Katz and Tiep (Airy sheaves of Laurent type: an introduction,https://web.math.princeton.edu/~nmk/kt31_11sept.pdf). In the present paper, we make use of that general theory to compute monodromy groups in some particularly simple families (in the sense of “simple to remember), realizing Weyl groups of type$$E_6$$ E 6 and$$E_8$$ E 8 . 
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    Free, publicly-accessible full text available December 1, 2025
  2. ; (, Journal of Pure and Applied Algebra)
    Free, publicly-accessible full text available September 1, 2025
  3. ; (, Mathematische Zeitschrift)
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  4. ; (, Geometric and Functional Analysis)
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  5. ; (, Cambridge Journal of Mathematics)
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  6. ; (, Journal of Algebra)
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  7. ; (, Advances in Mathematics)
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  8. ; ; (, Transactions of the American Mathematical Society)
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  9. ; ; (, International Journal of Number Theory)
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    We first develop some basic facts about hypergeometric sheaves on the multiplicative group [Formula: see text] in characteristic [Formula: see text]. Certain of their Kummer pullbacks extend to irreducible local systems on the affine line in characteristic [Formula: see text]. One of these, of rank [Formula: see text] in characteristic [Formula: see text], turns out to have the Conway group [Formula: see text], in its irreducible orthogonal representation of degree [Formula: see text], as its arithmetic and geometric monodromy groups. 
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  10. ; ; (, Journal of Number Theory)
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