The Néron component series of an abelian variety
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We introduce the Néron component series of an abelian variety A over a complete discretely valued field. This is a power series in ℤ[[T]], which measures the behaviour of the number of components of the Néron model of A under tame ramification of the base field. If A is tamely ramified, then we prove that the Néron component series is rational. It has a pole at T = 1, whose order equals one plus the potential toric rank of A. This result is a crucial ingredient of our proof of the motivic monodromy conjecture for abelian varieties. We expect that it extends to the wildly ramified case; we prove this if A is an elliptic curve, and if A has potential purely multiplicative reduction.
Originalsprog | Engelsk |
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Tidsskrift | Mathematische Annalen |
Vol/bind | 348 |
Udgave nummer | 3 |
Sider (fra-til) | 749-778 |
Antal sider | 30 |
ISSN | 0025-5831 |
DOI | |
Status | Udgivet - 8 mar. 2010 |
ID: 233909918