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L-functions of p-adic characters and geometric Iwasawa theory. (English) Zbl 0615.14013
This paper proves a geometric analog of the main conjecture of Iwasawa theory using étale cohomology. An application is then made to Igusa curves over \({\mathbb{F}}_ p\).
Reviewer: D.Goss

MSC:
14G15 Finite ground fields in algebraic geometry
14H25 Arithmetic ground fields for curves
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References:
[1] Adolphson, A.: Ap-adic theory of Hecke polynomials. Duke Math. J.43 (No. 1), 115-145 (1976) · Zbl 0339.14012
[2] Deligne, P.: Formes modulaires et representationsl-adiques. Sém. Bourb. 335. Lect. Notes Math., vol. 179, Berlin-Heidelberg-New York: Springer 1971 · Zbl 0206.49901
[3] Deligne, P., Rapoport, M.: Les schemas de nodules de courbes elliptiques. In: Modular forms of one variable II. Lect. Notes Math., vol. 349. Berlin-Heidelberg-New York: Springer 1973 · Zbl 0281.14010
[4] Dwork, B.: On Hecke polynomials. Invent. Math.12, 249-256 (1971) · Zbl 0219.14014
[5] Goss, D., Sinnot, W.: Class-groups of function fields. Duke Math. J.52 (No. 2), 507-516 (1985) · Zbl 0571.12006
[6] Hayes, D.: Analytic class number formulas in global function fields. Invent. Math.65, 49-69 (1981) · Zbl 0491.12014
[7] Hayes, D.: Stickelberger elements in function fields. Compos. Math.55, 209-239 (1985) · Zbl 0569.12008
[8] Illusie, L.: Complexe de De Rham-Witt et cohomologie cristalline. Ann. Sci. Ec. Norm. Super., IV. Ser.12, 501-661 (1979) · Zbl 0436.14007
[9] Katz, N.: Travaux de Dwork. Sem. Bourb. 409. Lect. Notes Math., vol. 317. Berlin-Heidelberg-New York: Springer 1973
[10] Katz, N.:P-adic properties of modular schemes and modular forms. In: Modular forms of one variable III. Lect. Notes. Math., vol. 350. Berlin-Heidelberg-New York: Springer 1973 · Zbl 0271.10033
[11] Katz, N., Messing, W.: Some consequences of the Riemann hypothesis for varieties over finite fields. Invent. Math.23, 73-77 (1974) · Zbl 0275.14011
[12] Mazur, B., Wiles, A.: Analogies between function fields and number fields. Am. J. Math.105 (No. 2), 507-521 (1983) · Zbl 0531.12015
[13] Serre, J-P.: Quelque propriétés des varietés abéliennes en caracteristiquep. Am. J. Math.80 (No. 3), 714-739 (1958) · Zbl 0099.16201
[14] Tate, J.: Les Conjectures de Stark sur les FonctionsL d’Artin ens=0. Boston: Birkhäuser 1984
[15] Washington, L.: Introduction to Cyclotomic Fields. Graduate texts in mathematics. Berlin-Heidelberg-New York: Springer 1982 · Zbl 0484.12001
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