The norm map on Jacobians
Abstract: Let be an unramified normal cover of smooth projective curves. Let be the induced map on Jacobians. Let be the kernel of and the connected component of . We prove that is isomorphic to where is the covering group of .
-  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 0067929, https://doi.org/10.2307/2372527
-  David Mumford, Curves and their Jacobians, The University of Michigan Press, Ann Arbor, Mich., 1975. MR 0419430
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Keywords: Jacobian, unramified cover, kernel of the norm map
Article copyright: © Copyright 1983 American Mathematical Society