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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



The norm map on Jacobians

Author: Michael Rosen
Journal: Proc. Amer. Math. Soc. 87 (1983), 19-22
MSC: Primary 14H30
MathSciNet review: 677222
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Abstract: Let $ \pi :\Gamma \to {\Gamma _0}$ be an unramified normal cover of smooth projective curves. Let $ {\pi _*}:J \to {J_0}$ be the induced map on Jacobians. Let $ H$ be the kernel of $ {\pi _*}$ and $ {H^0}$ the connected component of $ H$. We prove that $ H/{H^0}$ is isomorphic to $ G/[G,G]$ where $ G$ is the covering group of $ \Gamma /{\Gamma _0}$.

References [Enhancements On Off] (What's this?)

  • [1] J. Kawada and J. Tate, On the Galois cohomology of unramified extensions of function fields in one variable, Amer. J. Math. 77 (1955), 197-217. MR 0067929 (16:799f)
  • [2] D. Mumford, Curves and their Jacobians, Univ. of Michigan Press, Ann Arbor, 1975. MR 0419430 (54:7451)

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Keywords: Jacobian, unramified cover, kernel of the norm map
Article copyright: © Copyright 1983 American Mathematical Society

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