Journal of the American Mathematical Society

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$L$-functions of $\varphi $-sheaves and Drinfeld modules


Authors: Y. Taguchi and D. Wan
Journal: J. Amer. Math. Soc. 9 (1996), 755-781
MSC (1991): Primary 11G40
MathSciNet review: 1327162
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  • [An] Greg W. Anderson, 𝑡-motives, Duke Math. J. 53 (1986), no. 2, 457–502. MR 850546, 10.1215/S0012-7094-86-05328-7
  • [De] P. Deligne, Cohomologie étale, Lecture Notes in Mathematics, Vol. 569, Springer-Verlag, Berlin-New York, 1977. Séminaire de Géométrie Algébrique du Bois-Marie SGA 41\over2; Avec la collaboration de J. F. Boutot, A. Grothendieck, L. Illusie et J. L. Verdier. MR 0463174
  • [Dr] V. G. Drinfel′d, Moduli varieties of 𝐹-sheaves, Funktsional. Anal. i Prilozhen. 21 (1987), no. 2, 23–41 (Russian). MR 902291
  • [Dw] Bernard Dwork, On the rationality of the zeta function of an algebraic variety, Amer. J. Math. 82 (1960), 631–648. MR 0140494
  • [DS] B. Dwork and S. Sperber, Logarithmic decay and overconvergence of the unit root and associated zeta functions, Ann. Sci. École Norm. Sup. (4) 24 (1991), no. 5, 575–604. MR 1132758
  • [Fo] Jean-Marc Fontaine, Représentations 𝑝-adiques des corps locaux. I, The Grothendieck Festschrift, Vol. II, Progr. Math., vol. 87, Birkhäuser Boston, Boston, MA, 1990, pp. 249–309 (French). MR 1106901
  • [Fu] William Fulton, A note on weakly complete algebras, Bull. Amer. Math. Soc. 75 (1969), 591–593. MR 0238829, 10.1090/S0002-9904-1969-12250-0
  • [G1] David Goss, 𝐿-series of Grössencharakters of type 𝐴₀ for function fields, 𝑝-adic methods in number theory and algebraic geometry, Contemp. Math., vol. 133, Amer. Math. Soc., Providence, RI, 1992, pp. 119–139. MR 1183974, 10.1090/conm/133/1183974
  • [G2] David Goss, 𝐿-series of 𝑡-motives and Drinfel′d modules, The arithmetic of function fields (Columbus, OH, 1991) Ohio State Univ. Math. Res. Inst. Publ., vol. 2, de Gruyter, Berlin, 1992, pp. 313–402. MR 1196527
  • [G3] D. Goss, The adjoint of the Carlitz module and Fermat's last theorem, Finite fields and their applications 1 (1995), 165--188.
  • [Gr] A. Grothendieck, Formule de Lefschetz et rationalité des fonctions $L$, Séminaire Bourbaki, exposé 279, 1964/65. MR 33:54201
  • [SGA1] Revêtements étales et groupe fondamental, Springer-Verlag, Berlin-New York, 1971 (French). Séminaire de Géométrie Algébrique du Bois Marie 1960–1961 (SGA 1); Dirigé par Alexandre Grothendieck. Augmenté de deux exposés de M. Raynaud; Lecture Notes in Mathematics, Vol. 224. MR 0354651
  • [K1] Nicholas Katz, Travaux de Dwork, Séminaire Bourbaki, 24ème année (1971/1972), Exp. No. 409, Springer, Berlin, 1973, pp. 167–200. Lecture Notes in Math., Vol. 317 (French, with English summary). MR 0498577
  • [K2] Nicholas M. Katz, 𝑝-adic properties of modular schemes and modular forms, Modular functions of one variable, III (Proc. Internat. Summer School, Univ. Antwerp, Antwerp, 1972) Springer, Berlin, 1973, pp. 69–190. Lecture Notes in Mathematics, Vol. 350. MR 0447119
  • [K3] Groupes de monodromie en géométrie algébrique. II, Lecture Notes in Mathematics, Vol. 340, Springer-Verlag, Berlin-New York, 1973 (French). Séminaire de Géométrie Algébrique du Bois-Marie 1967–1969 (SGA 7 II); Dirigé par P. Deligne et N. Katz. MR 0354657
  • [Re] Daniel Reich, A 𝑝-adic fixed point formula, Amer. J. Math. 91 (1969), 835–850. MR 0255549
  • [S1] Jean-Pierre Serre, Groupes algébriques et corps de classes, Publications de l’institut de mathématique de l’université de Nancago, VII. Hermann, Paris, 1959 (French). MR 0103191
  • [S2] Jean-Pierre Serre, Endomorphismes complètement continus des espaces de Banach 𝑝-adiques, Inst. Hautes Études Sci. Publ. Math. 12 (1962), 69–85 (French). MR 0144186
  • [Ta] Y. Taguchi, A duality for finite $t$-modules, J. Math. Sci. Univ. Tokyo (to appear).
  • [Th] D. Thakur, On characteristic $p$ zeta functions, Compositio Math. (to appear).
  • [W1] D. Wan, Meromorphic continuation of $L$-functions of $p$-adic representations, Ann. of Math. (to appear).
  • [W2] D. Wan, Noetherian subrings of power series rings, Proc. Amer. Math. Soc 123 (1995), 1681--1686.

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Additional Information

Y. Taguchi
Affiliation: Department of Mathematics, Tokyo Metropolitan University, Hachioji, Tokyo 192-03, Japan
Email: taguchi@math.metro-u.ac.jp

D. Wan
Affiliation: Department of Mathematics, University of Nevada, Las Vegas, Nevada 89154
Email: wan@math.psu.edu

DOI: http://dx.doi.org/10.1090/S0894-0347-96-00199-3
Received by editor(s): December 8, 1994
Received by editor(s) in revised form: April 24, 1995
Additional Notes: The first author was partially supported by JSPS Postdoctoral Fellowships for Research Abroad.
The second author was partially supported by NSF and the UNLV Faculty Development Leave Committee.
Article copyright: © Copyright 1996 American Mathematical Society