A Herbrand-Ribet theorem for function fields

DOI10.1007/s00222-011-0346-3zbMath1278.11102arXiv1104.5363OpenAlexW1967150711MaRDI QIDQ421020

Lenny Taelman

Publication date: 23 May 2012

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1104.5363

zbMATH Keywords

Carlitz modulecyclotomic function fieldsBernoulli-Carlitz numbersBernoulli numbersHerbrand-Ribet theorem

Mathematics Subject Classification ID

Arithmetic theory of algebraic function fields (11R58) Cyclotomic function fields (class groups, Bernoulli objects, etc.) (11R60)

Related Items (15)

Twisted characteristic \(p\) zeta functions ⋮ Zeta-like multiple zeta values in positive characteristic ⋮ Multiplicative relations between coefficients of logarithmic derivatives of 𝔽_q-linear functions and applications ⋮ On a problem à la Kummer-Vandiver for function fields ⋮ Aspects of Iwasawa theory over function fields ⋮ Leading coefficient of the Goss Zeta value and p-ranks of Jacobians of Carlitz cyclotomic covers ⋮ On Geometric Iwasawa Theory and Special Values of Zeta Functions ⋮ Stickelberger series and main conjecture for function fields ⋮ Recent developments in the theory of Anderson modules ⋮ Arithmetic of function field units ⋮ Arithmetic of positive characteristic -series values in Tate algebras ⋮ Power sums of polynomials over finite fields and applications: a survey ⋮ Cauchy-Carlitz numbers ⋮ Iwasawa main conjecture for the Carlitz cyclotomic extension and applications ⋮ Arithmetic of characteristic p special L-values

Cites Work

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• The Carlitz shtuka
• Special \(L\)-values of Drinfeld modules
• Kummer's theory for function fields
• On regularity of small primes in function fields
• Class-groups of function fields
• The class number of cyclotomic function fields
• A modular construction of unramified p-extensions of \(\mathbb{Q}(\mu_p)\)
• Duality in the flat cohomology of curves
• Log-algebraicity of twisted \(A\)-harmonic series and special values of \(L\)-series in characteristic \(p\)
• Schémas en groupes de type $(p,\ldots,p)$
• Notes on étale cohomology of number fields
• Group schemes of prime order
• On Gekeler's conjecture for function fields

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