Monodromy groups of Kloosterman and hypergeometric sheaves

DOI10.1007/s00039-021-00578-0zbMath1485.11166OpenAlexW3197413395MaRDI QIDQ2232152

Nicholas M. Katz, Pham Hũ'u Tiêp

Publication date: 4 October 2021

Published in: Geometric and Functional Analysis. GAFA (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00039-021-00578-0

zbMATH Keywords

finite simple groupslocal systemsmonodromy groupshypergeometric sheaves

Mathematics Subject Classification ID

Linear algebraic groups over finite fields (20G40) Ordinary representations and characters (20C15) Exponential sums (11T23) Simple groups: alternating groups and groups of Lie type (20D06) Representations of finite groups of Lie type (20C33)

Related Items (1)

A rigid local system with monodromy group the big Conway group $2.\mathsf {Co}_1$ and two others with monodromy group the Suzuki group $6.{{Suz}}$

Uses Software

• GAP
• OEIS

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Large element orders and the characteristic of Lie-type simple groups.
• On the maximal subgroups of the finite classical groups
• Weil representations of finite general linear groups and finite special linear groups
• Symmetric powers and a problem of Kollár and Larsen.
• Local-to-global extensions of representations of fundamental groups
• On the monodromy groups attached to certain families of exponential sums
• Singer-Zyklen in klassischen Gruppen
• Torsion in reductive groups
• On the minimal degrees of characters of \(S_n\)
• On the minimal degree of a primitive permutation group
• Coverings of the affine line in characteristic \(p>0\) and Abhyankar's conjecture
• Abhyankar's conjecture on Galois groups over curves
• Some generalizations of the Weil representations of the symplectic and unitary groups
• Monodromy of Airy and Kloosterman sheaves
• Rigid local systems and alternating groups
• Automorphisms of extra special groups and nonvanishing degree 2 cohomology
• Cross characteristic representations of symplectic and unitary groups
• Étale Galois covers of affine smooth curves. The geometric case of a conjecture of Shafarevich. On Abhyankar's conjecture
• Unitary \(t\)-groups
• Rigid local systems and finite general linear groups
• Moments of Weil representations of finite special unitary groups
• Rigid local systems with monodromy group the Conway group \(\mathsf{Co}_3\)
• Rigid local systems and finite symplectic groups
• Local systems and finite unitary and symplectic groups
• A rigid local system with monodromy group \(2.J_{2}\)
• A problem of Kollár and Larsen on finite linear groups and crepant resolutions
• Seminar on algebraic groups and related finite groups. Held at the Institute for Advanced Study, Princeton/N.J., 1968/69
• The automorphism group of an extraspecial \(p\)-group
• On the maximum orders of elements of finite almost simple groups and primitive permutation groups
• Coverings of Algebraic Curves
• Majoration explicite de l'ordre maximum d'un élément du groupe symétrique
• Character Table and Blocks of Finite Simple Triality Groups 3 D 4 (q)
• Gauss Sums, Kloosterman Sums, and Monodromy Groups. (AM-116)
• Exponential Sums and Differential Equations. (AM-124)
• Lower bounds for the minima of certain symplectic and unitary group lattices
• On restrictions of modular spin representations of symmetric and alternating groups
• RIGID LOCAL SYSTEMS ON WITH FINITE MONODROMY
• Cross characteristic representations of even characteristic symplectic groups
• Minimal characters of the finite classical groups
• The largest irreducible representations of simple groups
• Exponential sums and total Weil representations of finite symplectic and unitary groups
• A rigid local system with monodromy group the big Conway group $2.\mathsf {Co}_1$ and two others with monodromy group the Suzuki group $6.{{Suz}}$
• Rigid local systems with monodromy group the Conway group Co2
• Symmetric and alternating powers of Weil representations of finite symplectic groups
• PRIMITIVE PERMUTATION GROUPS CONTAINING A CYCLE
• Rational irreducible characters and rational conjugacy classes in finite groups

This page was built for publication: Monodromy groups of Kloosterman and hypergeometric sheaves