Trace formula for component groups of Néron models

Details Trace formula for component groups of Néron models Trace formula for component groups of Néron models

2009-01-13

arxiv.org/abs/0901.1809v2

Mathematics

Algebraic Geometry

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

Scientific paper

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 N\'eron model of $A$ in terms of the Galois action on the $\ell$-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 N\'eron model.

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