English

Trace formula for component groups of N\'eron models

Algebraic Geometry 2009-05-22 v2

Abstract

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

Keywords

Cite

@article{arxiv.0901.1809,
  title  = {Trace formula for component groups of N\'eron models},
  author = {Johannes Nicaise},
  journal= {arXiv preprint arXiv:0901.1809},
  year   = {2009}
}

Comments

Main result (Conjecture 1.1) proven unconditionally; Conjecture 1.2 in version 1 was recently proven by Liu and Lorenzini (see [10])

R2 v1 2026-06-21T12:00:17.525Z