Abstract
In this chapter, we assume that k is algebraically closed. We will compare the base change conductor of the Jacobian variety of a K-curve C to the Artin conductor of C and other invariants of the curve, assuming that the genus of C is 1 or 2.
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C.-L. Chai, Néron models for semiabelian varieties: congruence and change of base field. Asian J. Math. 4(4), 715–736 (2000)
C.-L. Chai, J.-K. Yu, Congruences of Néron models for tori and the Artin conductor (with an appendix by E. de Shalit). Ann. Math. (2) 154, 347–382 (2001)
L.H. Halle, J. Nicaise, The Néron component series of an abelian variety. Math. Ann. 348(3), 749–778 (2010)
Q. Liu, Conducteur et discriminant minimal de courbes de genre 2. Compos. Math. 94(1), 51–79 (1994)
D. Lorenzini, Models of curves and wild ramification. Appl. Math. Q. 6(1), 41–82 (2010). Special Issue in honor of John Tate. Part 2
T. Saito, Vanishing cycles and geometry of curves over a discrete valuation ring. Am. J. Math. 109(6), 1043–1085 (1987)
T. Saito, Conductor, discriminant, and the Noether formula of arithmetic surfaces. Duke Math. J. 57(1), 151–173 (1988)
T. Saito, The discriminants of curves of genus 2. Compos. Math. 69(2), 229–240 (1989)
J.H. Silverman, The Arithmetic of Elliptic Curves. Graduate Texts in Mathematics, vol. 106 (Springer, New York, 1986)
J.H. Silverman, Advanced Topics in the Arithmetic of Elliptic Curves. Graduate Texts in Mathematics, vol. 151 (Springer, New York, 1994)
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Halle, L.H., Nicaise, J. (2016). The Base Change Conductor and the Artin Conductor. In: Néron Models and Base Change. Lecture Notes in Mathematics, vol 2156. Springer, Cham. https://doi.org/10.1007/978-3-319-26638-1_7
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DOI: https://doi.org/10.1007/978-3-319-26638-1_7
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