The norm map on Jacobians
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- by Michael Rosen PDF
- Proc. Amer. Math. Soc. 87 (1983), 19-22 Request permission
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
- Y. 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 67929, DOI 10.2307/2372527
- David Mumford, Curves and their Jacobians, University of Michigan Press, Ann Arbor, Mich., 1975. MR 0419430
Additional Information
- © Copyright 1983 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 87 (1983), 19-22
- MSC: Primary 14H30
- DOI: https://doi.org/10.1090/S0002-9939-1983-0677222-8
- MathSciNet review: 677222