EXPLICIT DETERMINATION OF ROOT NUMBERS OF ABELIAN VARIETIES

Let A be an abelian variety over a nonarchimedean local field of definition K and let W(A) be the root number of A. Let F be a Galois extension of K over which A has semistable reduction, allowing F = K. We analyze W(A) in terms of contributions from the toric and abelian variety components of the closed fibers of the Neron models of A over the ring of integers of K and of F. In particular, our results can be used to calculate W(A) in two main instances: first, for abelian varieties with additive reduction over K and totally toroidal reduction over F, provided that the residue characteristic of K is odd; second, for the Jacobian A = J(C) of a stable curve C over K.