Good reduction of abelian varieties

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COMPUTING L-FUNCTIONS AND SEMISTABLE REDUCTION OF SUPERELLIPTIC CURVES (2012, background): “) ∼=V(Pic0(Y¯)), where Vℓ(·) denotes the rational ℓ-adic Tate module. Let Jdenote the N´eron model of the Jacobian of Yand J¯0 the connected component of its special ﬁber. Then by [11], 6.4 (see also [24], Lemma 2) we have (2.4) Vℓ(Pic0(Y))IK ∼=Vℓ(J¯0). Under the conditions imposed on Ywe have an is”
The index of an algebraic variety (2012, methodology): “Then B is an Abelian scheme ([52], Corollary 2 to Theorem 1).”
Lectures on K3 Surfaces (2016, background): “2]) and by Néron–Ogg–Šafarevič theory (see [547]), the inertia group acts trivially on H1 ét(AK̄ ,Z`) if and only if A reduces to a smooth abelian variety A0 over k for which there then exists an isomorphism”
Local invariants of isogenous elliptic curves (2012, background): “ Galois extension of Knr where E has good reduction. The Galois group Gal(F/Knr) has order at least 3, since E is not a quadratic twist of a curve with good reduction (cf. Lemma A.3). As explained in [21] proof of Thm. 2, it acts faithfully on the reduced curve E˜ deﬁned over the residue ﬁeld of F a”