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On the Kolyvagin cup product

Author(s): Amnon Besser
Journal: Trans. Amer. Math. Soc. 349 (1997), 4635-4657.
MSC (1991): Primary 11R34; Secondary 18G15
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Abstract: We define a new cohomological operation, which we call the Kolyvagin cup product, that is a generalization of the derivative operator introduced by Kolyvagin in his work on Euler systems. We show some of the basic properties of this operation. We also define a higher dimensional derivative in certain cases and a dual operation which we call the Kolyvagin cap product and which generalizes a computation of Rubin.

References:

[Dar92]: Henri Darmon, A refined conjecture of Mazur-Tate type for Heegner points, Invent. Math. 110 (1992), no. 1, 123-146. MR 93i:11066
[Kol90]: Victor A. Kolyvagin, Euler systems, The Grothendieck Festschrift vol. II, Prog. Math., vol. 87, Birkhäuser, Boston, Basel, Berlin, 1990, pp. 435-483. MR 92g:11109
[Mil86]: James S. Milne, Arithmetic duality theorems, Perspectives in Mathematics, Academic Press, 1986. MR 88e:14028
[Nek92]: Jan Neková\v{r}, Kolyvagin's method for Chow groups of Kuga-Sato varieties, Invent. Math. 107 (1992), no. 1, 99-125. MR 93b:11076
[Rub93]: Karl Rubin, Abelian varieties, -adic heights and derivatives, Algebra and Number Theory (Essen, 1992; G. Frey and J. Ritter, editors), de Gruyter, Berlin, 1994, pp. 247-266. MR 95i:11066

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Additional Information:

Amnon Besser
Affiliation: Department of Mathematics, University of California at Los Angeles, Box 951555, Los Angeles, California 90095-1555
Address at time of publication: Department of Mathematical Sciences, University of Durham, Science Laboratories, South Road, Durham, DH1 3LE, United Kingdom

DOI: 10.1090/S0002-9947-97-01777-7
PII: S 0002-9947(97)01777-7
Received by editor(s): May 16, 1995
Received by editor(s) in revised form: April 11, 1996
Additional Notes: Partially supported by an NSF grant
Copyright of article: Copyright 1997, American Mathematical Society


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