Morita's conjecture on potentially good reduction of abelian varieties

Let EE) be a number field, let A/EA/E be an abelian variety, and let MT(A)\mathrm{MT}(A) 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 MT(A)\mathrm{MT}(A) contains no nontrivial unipotent Q\mathbb{Q}-rational point, then AA has potentially good reduction at every finite prime of EE. 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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