Notes on an analogue of the Fontaine-Mazur conjecture
Jeffrey D. Achter; Joshua Holden
Journal de théorie des nombres de Bordeaux (2003)
- Volume: 15, Issue: 3, page 627-637
- ISSN: 1246-7405
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top- [1] N. Boston, Some cases of the Fontaine-Mazur conjecture, II. J. Number Theory75 (1999), 161-169. Zbl0928.11050MR1681626
- [2] N. Chavdarov, The generic irreducibility of the numerator of the zeta function in a family of curves with large monodromy. Duke Math. J.87 (1997), 151-180. Zbl0941.14006MR1440067
- [3] A.J. De Jong, A conjecture on arithmetic fundamental groups. Israel J. Math.121 (2001), 61-84. Zbl1054.11032MR1818381
- [4] P. Deligne, La conjecture de Weil. II. Hautes Études Sci. Publ. Math.52 (1980), 137-252. Zbl0456.14014MR601520
- [5] P. Deligne, D. Mumford, The irreducibility of the space of curves of given genus. Inst. Hautes Études Sci. Publ. Math.36 (1969), 75-109. Zbl0181.48803MR262240
- [6] J. Dixon, M.P.F. Du Sautoy, A. Mann, D. Segal, Analytic Pro-p Groups. London Math. Soc. Lecture Note Series.157 (1991). Zbl0744.20002
- [7] T. Ekedahl, The action of monodromy on torsion points of Jacobians. Arithmetic algebraic geometry (Texel, 1989). BirkhäuserBoston (1991), 41-49. Zbl0728.14028MR1085255
- [8] J.-M. Fontaine, B. Mazur, Geometric Galois representations. J. Coates and S.-T. Yau, editors, Elliptic Curves, Modular Forms, & Fermat's Last Theorem, Series in Number Theory1 (1995), 41-78. Zbl0839.14011MR1363495
- [9] G. Frey, E. Kani, H. Völklein, Curves with infinite K-rational geometric fundamental group. H. Völklein, D. Harbater, P. Müller, and J. G. Thompson, editors, Aspects of Galois theory (Gainesville, FL, 1996), London Mathematical Society Lecture Note Series256, 85-118. Zbl0978.14021MR1708603
- [10] J. Holden, On the Fontaine-Mazur Conjecture for number fields and an analogue for function fields. J. Number Theory81 (2000), 16-47. Zbl0997.11096MR1743506
- [11] Y. Ihara, On unramified extensions of function fields over finite fields. Y. Ihara, editor, Galois Groups and Their Representations, Adv. Studies in Pure Math.2 (1983), 89-97. Zbl0542.14011MR732464
- [12] N.M. Katz, P. Sarnak, Random matrices, Frobenius eigenvalues, and monodromy. American Mathematical Society, 1999. Zbl0958.11004MR1659828