The χ-part of the Analytic Class Number Formula, for Global Function Fields

• Autorzy: Viguié S.

Identyfikatory

DOI

10.4064/ba60-2-2

• Języki publikacji: EN

Abstrakty

EN

Let F/k be a finite abelian extension of global function fields, totally split at a distinguished place ∞ of k. We show that a complex Gras conjecture holds for Stark units, and we derive a refined analytic class number formula.

Słowa kluczowe

EN

Stark units; Gras conjecture; analytic class number formula

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2012
• Tom: Vol. 60, no 2
• Strony: 113--122
• Opis fizyczny: Bibliogr. 11 poz.

Twórcy

autor

Viguié S.

• Laboratoire de Mathematiques de Besancon UMR CNRS 6623 Universite de Franche-Comte 16 route de Gray 25030 Besancon Cedex, France

Bibliografia

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• [3] -, Congruences between derivatives of geometric L-functions, ibid. 184 (2011), 221-256.
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• [6] -, Construction of elliptic units in function fields, in: Number Theory, S. David (ed.), Cambridge Univ. Press, 1995, 187-208.
• [7] H. Oukhaba and S. Viguie, The Gras conjecture in function fields by Euler systems, Bull. London Math. Soc. 43 (2011), 523-535.
• [8] C. D. Popescu, Gras-type conjectures for function fields, Compos. Math. 118 (1999), 263-290.
• [9] -, On a rened Stark conjecture for function fields, ibid. 116 (1999), 321-367.
• [10] J. Tate, Les Conjectures de Stark sur les Fonctions L d'Artin en s = 0, Progr. Math. 47, Birkhäuser, 1984.
• [11] S. Viguie, Index-modules and applications, Manuscripta Math. 136 (2011), 445-460.