Morita's conjecture on potentially good reduction of abelian varieties
Morita's conjecture on potentially good reduction of abelian varieties
Let ) be a number field, let be an abelian variety, and let denote its Mumford–Tate group. A point of an algebraic group is unipotent if it is unipotent in a faithful linear representation. Morita's conjecture. If contains no nontrivial unipotent -rational point, then has potentially good reduction at every finite prime of . This conjecture relates the unipotent radical of the Mumford–Tate group to the reduction of an abelian variety; the source gives no resolution status.
Sources & referencesView supporting material
Primary source
Frederic Paugam, “Galois representations, Mumford-Tate groups and good reduction of abelian varieties”, arXiv:math/0302117 (2004).
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