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 over a complete discretely valued field, which expresses the Euler characteristic of the special fiber of the N\'eron model of in terms of the Galois action on the -adic cohomology of . If 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])