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Iwasawa-theory of abelian varieties at primes of non-ordinary reduction

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Abstract

We explain how to associate to an abelian variety over ℚ with good and non-ordinary reduction atp a submodule of some power of a ring of analytic functions over the Iwasawa-algebra. From this construction formulas about the size of the Selmer groups over the the cyclotomic ℤ p of ℚ are deduced.

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References

  • [CS]Cornell, G. andSilverman, J.H.: Arithmetic geometry. Springer 1986

  • [De]Demazure, M.: Lectures on p-divisible groups. Lecture Notes in Math.302. Springer 1972.

  • [Fo]Fontaine, J.-M.: Groupes p-divisibles sur les corps locaux. Asterisque47–48 (1977)

  • [Gr]Greenberg, R.: Iwasawa theory forp-adic representations. Adv. Stud. Pure Math.17 (1989)

  • [Ka]Kato, K.: Lectures on the approach to Iwasawa theory for Hasse-Weil L-functiones viaB dR. In: Lecture Notes in Math.1553, pp. 50–163. Springer 1994

  • [Katz]Katz, N.: Slope Filtration of F-Crystals. Asterisque63, 113–164 (1979)

    MATH  Google Scholar 

  • [Man]Manin, J.: Cyclotomic fields and modular curves. Russ. Math. Surv.26, 7–78 (1971)

    Article  MATH  MathSciNet  Google Scholar 

  • [Maz]Mazur, B.: Rational points of abelian varieties with values in towers of number fields. Inv. Math.18, 183–266 (1972)

    Article  MATH  MathSciNet  Google Scholar 

  • [MTT]Mazur, B., Tate, J. andTeitelbaum, J.: On p-adic analogues of the conjectures of Birch and Swinnerton-Dyer, Inv. Math.84, 1–48 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  • [Mi1]Milne, J.S.: Étale Cohomology. Princeton University Press 1980

  • [Mi2]Milne, J.S.: Arithmetic Duality Theorems. Academic Press 1986

  • [PR1]Perrin-Riou, B.: Théorie d’Iwasawa p- adique locale et globale. Inv. Math.99, 247–292 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  • [PR2]Perrin-Riou, B.: Fonctions L p-adiques d’une courbe elliptique et points rationnels. Ann. Inst. Fourier Grenoble43, 945–995 (1993)

    MATH  MathSciNet  Google Scholar 

  • [PR3]Perrin-Riou, B.: Théorie d’Iwasawa des representations p-adique sur un corps local. Inv. Math.115, 81–149 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  • [Sch1]Schneider, P.: Iwasawa L-Functions of Varieties over Algebraic Number Fields. Inv. Math.71, 251–293 (1983)

    Article  MATH  Google Scholar 

  • [Sch2]Schneider, P.: p-adic height pairings. II. Inv. Math.79, 329–374 (1985)

    Article  MATH  Google Scholar 

  • [Sch3]Schneider, P.: Arithmetic of formal groups and applications I: Universal norm subgroups. Inv. Math.87, 587–602 (1987)

    Article  MATH  Google Scholar 

  • [CL]Serre, J.-P.: Corps locaux. Hermann, Paris 1962

    MATH  Google Scholar 

  • [Ta1]Tate, J.: WC-Groups over p-adic Fields. Sem. Bourbaki156, 1–13 (1957)

    Google Scholar 

  • [Ta2]Tate, J.: p-divisible Groups. In: Proc. Conf. Local Fields, Driebergen 1966, pp. 158–183. Springer 1967

  • [Vi]Visik, M.M.: Non-archimedean measures connected with Dirichlet series. Math. USSR Sbornik Vol.28 (1976)

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  1. Mathematisches Institut, Westfälische Wilhelms-Universität Münster, Einsteinstr. 62, D 48149, Münster, Germany

    Heiko Knospe

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  1. Heiko Knospe
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Knospe, H. Iwasawa-theory of abelian varieties at primes of non-ordinary reduction. Manuscripta Math 87, 225–258 (1995). https://doi.org/10.1007/BF02570472

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