2016
DOI: 10.1007/978-3-319-26638-1
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Néron Models and Base Change

Abstract: Abstract. We study various aspects of the behaviour of Néron models of semi-abelian varieties under finite extensions of the base field, with a special emphasis on wildly ramified Jacobians. In Part 1, we analyze the behaviour of the component groups of the Néron models, and we prove rationality results for a certain generating series encoding their orders. In Part 2, we discuss Chai's base change conductor and Edixhoven's filtration, and their relation to the Artin conductor. All of these results are applied … Show more

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Cited by 19 publications
(42 citation statements)
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“…Since we already know that #Φ(Ñ (α + qe(C))) tors = ((α + qe(C))/α ′ ) t(Pic 0 C/K × K K(α ′ )) #Φ(Ñ (α ′ )) tors by [13], Proposition 4.3.1.1, the result follows from Proposition 6.11. These two observations together imply the result.…”
Section: Applications To Motivic Zeta Functionsmentioning
confidence: 78%
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“…Since we already know that #Φ(Ñ (α + qe(C))) tors = ((α + qe(C))/α ′ ) t(Pic 0 C/K × K K(α ′ )) #Φ(Ñ (α ′ )) tors by [13], Proposition 4.3.1.1, the result follows from Proposition 6.11. These two observations together imply the result.…”
Section: Applications To Motivic Zeta Functionsmentioning
confidence: 78%
“…Proof. By Proposition 7.2, [13], Theorem 6.3.1.3, and [13], Corollary 6.3.1.5, all we have to show is that the exact sequence Here we use that Pic 0 C/K × K Spec K(d) = Pic 0 C× K Spec K(d)/K(d) (and similarly forC), that the curve C × K Spec K(d) still has a push-out singularity by Lemma 4.3, and that L⊗ K K(d) is a field whenever d is prime to p[L : K]. Further, we use that (Res L/K G m )/ G m × K Spec K(d) = (Res L⊗ K K(d)/K(d) G m )/ G m , and Theorem 6.6.…”
Section: Applications To Jumpsmentioning
confidence: 87%
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“…However, the situation becomes much more subtle if the residual characteristic is positive: Nicaise proved the equality (1) if X is a curve [16, §7], and Halle-Nicaise handled the case of a semi-abelian variety [9,Chapter 8].…”
mentioning
confidence: 99%