The generic irreducibility of the numerator of the zeta function in a family of curves with large monodromy

DOI10.1215/S0012-7094-97-08707-XzbMath0941.14006MaRDI QIDQ1355295

Nick Chavdarov

Publication date: 26 July 2000

Published in: Duke Mathematical Journal (Search for Journal in Brave)

zbMATH Keywords

finite ground fieldfamily of curvesKatz's conjecturelarge monodromynumerator of the zeta function

Mathematics Subject Classification ID

Finite ground fields in algebraic geometry (14G15) Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) (14G10) (L)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture (11G40)

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Cites Work

• On subgroups of \(GL_ n(F_ p)\)
• La conjecture de Weil. II
• Cohomologie étale. Seminaire de géométrie algébrique du Bois-Marie SGA 4 1/2 par P. Deligne, avec la collaboration de J. F. Boutot, A. Grothendieck, L. Illusie et J. L. Verdier
• Conjugacy classes in algebraic groups. Notes by Vinay V. Deodhar
• Good reduction of abelian varieties
• Algebraic Groups Over Finite Fields
• Gauss Sums, Kloosterman Sums, and Monodromy Groups. (AM-116)
• Galois Action on Division Points of Abelian Varieties with Real Multiplications
• Endomorphisms of linear algebraic groups
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item