[PDF][PDF] Exponential sums, hypergeometric sheaves, and monodromy groups
NM Katz, PH Tiep - Annals of Mathematics Studies. Princeton …, 2025 - math.princeton.edu
The study of exponential sums over finite fields goes back to Gauss. The importance of
estimating them goes back at least to Kloosterman's 1926 paper [Kl]. In the one-variable …
estimating them goes back at least to Kloosterman's 1926 paper [Kl]. In the one-variable …
Monodromy groups of Kloosterman and hypergeometric sheaves
NM Katz, PH Tiep - Geometric and Functional Analysis, 2021 - Springer
We study the possible structures of monodromy groups of Kloosterman and hypergeometric
sheaves on G _m G m in characteristic p. We show that most such sheaves satisfy a certain …
sheaves on G _m G m in characteristic p. We show that most such sheaves satisfy a certain …
Rigid local systems with monodromy group the Conway group Co3
NM Katz, A Rojas-León, PH Tiep - Journal of Number Theory, 2020 - Elsevier
We first develop some basic facts about certain sorts of rigid local systems on the affine line
in characteristic p> 0. We then apply them to exhibit a number of rigid local systems of rank …
in characteristic p> 0. We then apply them to exhibit a number of rigid local systems of rank …
[HTML][HTML] A rigid local system with monodromy group 2. J2
NM Katz, A Rojas-León - Finite Fields and Their Applications, 2019 - Elsevier
A rigid local system with monodromy group 2.J2 - ScienceDirect Skip to main contentSkip to
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A rigid local system with monodromy group the big Conway group 2. 𝖢𝗈₁ and two others with monodromy group the Suzuki group 6. 𝖲𝗎𝗓
N Katz, A Rojas-León, P Tiep - Transactions of the American Mathematical …, 2020 - ams.org
We first develop some basic facts about hypergeometric sheaves on the multiplicative group
$\mathbb {G} _m $ in characteristic $ p> 0$. Specializing to some special classes of …
$\mathbb {G} _m $ in characteristic $ p> 0$. Specializing to some special classes of …
Rigid local systems with monodromy group the Conway group
NM Katz, A Rojas-León, PH Tiep - International Journal of Number …, 2020 - World Scientific
We first develop some basic facts about hypergeometric sheaves on the multiplicative group
𝔾 m in characteristic p> 0. Certain of their Kummer pullbacks extend to irreducible local …
𝔾 m in characteristic p> 0. Certain of their Kummer pullbacks extend to irreducible local …
Monodromy groups of certain Kloosterman and hypergeometric sheaves
NM Katz, PH Tiep - arXiv preprint arXiv:2005.09051, 2020 - arxiv.org
A certain" condition (S)" on reductive algebraic groups was introduced in [GT2], in which a
slightly stronger condition (S+) was shown to have very strong consequences. We show that …
slightly stronger condition (S+) was shown to have very strong consequences. We show that …