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arXiv · 1303.0423

A refinement of the Artin conductor and the base change conductor

Ching-Li Chai·Christian Kappen
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Abstract

For a local field K with positive residue characteristic p, we introduce, in the first part of this paper, a refinement bAr_K of the classical Artin distribution Ar_K. It takes values in cyclotomic extensions of Q which are unramified at p, and it bisects Ar_K in the sense that Ar_K is equal to the sum of bAr_K and its conjugate distribution. Compared with 1/2 Ar_K, the bisection bAr_K provides a higher resolution on the level of tame ramification. In the second part of this article, we prove that the base change conductor c(T) of an analytic K-torus T is equal to the value of bAr_{K} on the Q_p-rational Galois representation X^*(T)_{Q_p} that is given by the character module X^*(T) of T. We hereby generalize a formula for the base change conductor of an algebraic K-torus, and we obtain a formula for the base change conductor of a semiabelian K-variety with potentially ordinary reduction.

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Ching-Li Chai, Christian Kappen. 2013-03-02. A refinement of the Artin conductor and the base change conductor. https://arxiv.org/abs/1303.0423

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