Trace formula for component groups of Néron models

2009/01/13 by Johannes Nicaise, Nicaise, Johannes · 1 citation
Mathematics · Pharmacology, Toxicology and Pharmaceutics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Alkaloids: synthesis and pharmacology #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.0901.1809

openalex publication_date 2009/01/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study a trace formula for tamely ramified abelian varieties A over a complete discretely valued field, which expresses the Euler characteristic of the special fiber of the Néron model of A in terms of the Galois action on the ℓ-adic cohomology of A. If A has purely additive reduction, the trace formula yields a cohomological interpretation for the number of connected components of the special fiber of the Néron model.

Citations

• A trace formula for varieties over a discretely valued field

Cited by

• Motivic zeta functions of abelian varieties, and the monodromy conjecture

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• The Néron component series of an abelian variety
• Galois actions on Neron models of Jacobians
• On the prime-to-p part of the groups of connected components of Néron models
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• Canonical extensions of Néron models of Jacobians