Abstract
In this chapter, we assume that k is algebraically closed. Let C be a smooth, proper, geometrically connected curve over K. We will study the behaviour of sncd-models of C under finite tame extensions of the base field K. Our main technical result is that these models can be compared in a very explicit way if the degree of the base change is prime to the stabilization index e(C) of C, a new invariant that we introduce in Definition 4.2.2.3. Using this result, we prove the rationality of the Néron component series of a Jacobian variety over K (Theorem 4.3.1.5).
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Halle, L.H., Nicaise, J. (2016). Models of Curves and the Néron Component Series of a Jacobian. In: Néron Models and Base Change. Lecture Notes in Mathematics, vol 2156. Springer, Cham. https://doi.org/10.1007/978-3-319-26638-1_4
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DOI: https://doi.org/10.1007/978-3-319-26638-1_4
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