Néron models, Lie algebras, and reduction of curves of genus one

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Motivic zeta functions of abelian varieties, and the monodromy conjecture (2009, background): “If V 1 and V 2 are (right) R [ μ ] -modules of ﬁnite type, free over R , and To see this, take any morphism of R -modules φ : It is an isomorphism since its reduction modulo π is the isomorphism ϕ This implies that we can lift the k -basis { v i,j } of Lie (X s ) to an R -basis { w i,j } of Lie ( G…”
On the Brauer group of a surface (2005, background): “The formula |X(A)|∏v δvδ′ v = δ2|Br(X)| is known to hold independently of the Kato-Trihan result [6] only when the periods δ′ v are pairwise coprime ([8], 4.”