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The -invariant change for abelian varieties over finite -extensions of global fields
We extend the work of Lai, Longhi, Suzuki, the first two authors and study
the change of -invariants, with respect to a finite Galois p-extension
, of an ordinary abelian variety over a -extension of
global fields (whose characteristic is not necessarily positive) that
ramifies at a finite number of places at which has ordinary reductions. We
obtain a lower bound for the -invariant of along and deduce
that the -invariant of an abelian variety over a global field can be
chosen as big as needed. Finally, in the case of elliptic curve over a global
function field that has semi-stable reduction everywhere we are able to improve
the lower bound in terms of invariants that arise from the supersingular places
of and certain places that split completely over .Comment: 31 page
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