References
Bosch, S., Lütkebohmert, W., Raynaud, M.: Néron models. Ergebnisse der Mathematik und ihrer Grenzgebiete, Springer-Verlag, Berlin, 1990
Cassels, J.W.S.: Arithmetic on curves of genus 1 (VIII). On the conjectures of Birch and Swinnerton-Dyer. J. Reine Angrew. Math. 217, 180–189 (1965)
Curtis, C.W., Reiner, I.: Methods of representation theory I. A Wiley-Interscience Publication, New York, 1990
Gonzalez-Avilés, C.D.: On the conjecture of Birch and Swinnerton-Dyer. Trans. Amer. Math. Soc. 349, 4181–4200 (1997)
Kani, E.: Relations between the genera and between the Hasse-Witt invariants of Galois coverings of curves. Canad. Math. Bull. Vol. 28, 321–327 (1985)
Kani, E., Rosen, M.: Idempotent relations and factors of Jacobians. Math. Ann. 284, 307–327 (1989)
Kani, E., Rosen, M.: Idempotent relations among arithmetic invariants attached to number fields and algebraic varieties. J. Number Theory 46, 230–254 (1994)
Kida, M.: Galois descent and twists of an abelian variety. Acta Arith. 73, 51–57 (1995)
Milne, J.S.: On the arithmetic of abelian varieties. Inventiones Math. 17, 177–190 (1972)
Mumford, D.: Abelian varieties. Oxford U.P., London, 1970
Park, H.: Idempotent relations and the conjecture of Birch and Swinnerton–Dyer. In: Algebra and Topology 1990 (Taejon, 1990), pp. 97–125
Rosen, M.I.: Some confirming instances of the Birch-Swinnerton-Dyer conjecture over biquadratic fields. In: Number Theory Proceedings of the First Conference of the Canadian Number Theory Association. R. A. Mollin (Eds.). Walter de Gruyter 1990
Silverman, J.: The Arithmetic of Elliptic Curves. Grad. Texts in Math. 106. Springer-Verlag 1986
Tate, J.: On the conjectures of Birch and Swinnerton–Dyer and a geometric analog. In: Séminaire Bourbaki, 1965–66, exposé 306
Weil, A.: Adeles and algebraic groups. Progress in Math. vol. 23, Birkhauser 1982
Weil, A.: Foundations of Algebraic Geometry. AMS Colloquium Publications, Providence, 1962
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Yu, H. Idempotent relations and the conjecture of Birch and Swinnerton-Dyer. Math. Ann. 327, 67–78 (2003). https://doi.org/10.1007/s00208-003-0427-8
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00208-003-0427-8