𝐿-functions of 𝜑-sheaves and Drinfeld modules

Taguchi, Y.; Wan, D.

doi:10.1090/S0894-0347-96-00199-3

$L$-functions of $\varphi$-sheaves and Drinfeld modules
HTML articles powered by AMS MathViewer

by Y. Taguchi and D. Wan PDF

J. Amer. Math. Soc. 9 (1996), 755-781 Request permission

References

Greg W. Anderson, $t$-motives, Duke Math. J. 53 (1986), no. 2, 457–502. MR 850546, DOI 10.1215/S0012-7094-86-05328-7
P. Deligne, Cohomologie étale, Lecture Notes in Mathematics, vol. 569, Springer-Verlag, Berlin, 1977 (French). Séminaire de géométrie algébrique du Bois-Marie SGA $4\frac {1}{2}$. MR 463174, DOI 10.1007/BFb0091526
V. G. Drinfel′d, Moduli varieties of $F$-sheaves, Funktsional. Anal. i Prilozhen. 21 (1987), no. 2, 23–41 (Russian). MR 902291
Bernard Dwork, On the rationality of the zeta function of an algebraic variety, Amer. J. Math. 82 (1960), 631–648. MR 140494, DOI 10.2307/2372974
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, DOI 10.24033/asens.1637
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
William Fulton, A note on weakly complete algebras, Bull. Amer. Math. Soc. 75 (1969), 591–593. MR 238829, DOI 10.1090/S0002-9904-1969-12250-0
David Goss, $L$-series of Grössencharakters of type $A_0$ 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, DOI 10.1090/conm/133/1183974
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
D. Goss, The adjoint of the Carlitz module and Fermat’s last theorem, Finite fields and their applications 1 (1995), 165–188.
Charles Hopkins, An extension of a theorem of Remak, Ann. of Math. (2) 40 (1939), 636–638. MR 33, DOI 10.2307/1968948
Revêtements étales et groupe fondamental, Lecture Notes in Mathematics, Vol. 224, 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. MR 0354651
Nicholas Katz, Travaux de Dwork, Séminaire Bourbaki, 24ème année (1971/1972), Exp. No. 409, Lecture Notes in Math., Vol. 317, Springer, Berlin, 1973, pp. 167–200 (French, with English summary). MR 0498577
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) Lecture Notes in Math., Vol. 350, Springer, Berlin, 1973, pp. 69–190. MR 0447119
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
Daniel Reich, A $p$-adic fixed point formula, Amer. J. Math. 91 (1969), 835–850. MR 255549, DOI 10.2307/2373354
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
Jean-Pierre Serre, Endomorphismes complètement continus des espaces de Banach $p$-adiques, Inst. Hautes Études Sci. Publ. Math. 12 (1962), 69–85 (French). MR 144186, DOI 10.1007/BF02684276
Y. Taguchi, A duality for finite $t$-modules, J. Math. Sci. Univ. Tokyo (to appear).
D. Thakur, On characteristic $p$ zeta functions, Compositio Math. (to appear).
D. Wan, Meromorphic continuation of $L$-functions of $p$-adic representations, Ann. of Math. (to appear).
D. Wan, Noetherian subrings of power series rings, Proc. Amer. Math. Soc 123 (1995), 1681–1686.