Trace formula for component groups of Néron models

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 $\ell$-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 Néron model.

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

References in corpus (2)

• A trace formula for rigid varieties, and motivic Weil generating series for formal schemes
• A trace formula for varieties over a discretely valued field

Cited by in corpus (1)

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