Schémas en groupes de type $(p,\ldots,p)$

Abstract

Schémas en groupes de type (p,. .. , p) Bulletin de la S. M. F., tome 102 (1974), p. 241-280 <http://www.numdam.org/item?id=BSMF_1974__102__241_0> © Bulletin de la S. M. F., 1974, tous droits réservés. L'accès aux archives de la revue « Bulletin de la S. M. F. » (http: //smf.emath.fr/Publications/Bulletin/Presentation.html) implique l'accord avec les conditions générales d'utilisation (http://www.numdam.org/ conditions). Toute utilisation commerciale ou impression systématique est constitutive d'une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques http://www.numdam.org/

An alternative description of the Drinfeld $p$-adic half-plane

“…In other words, Ker λ is a kgroup scheme of height one, in the sense of Raynaud [9]. (λ.b) If E/F is ramified, we ask that λ be a principal polarization.…”

Abelian varieties over cyclotomic fields with good reduction everywhere

“…This implies that [L : K] divides 3 and the proof in this case is complete. 15 ) is 1 and since the multiplicative group F * 81 of the residue field of the unique prime over 3 is generated by the units ζ 15 and 1 − ζ 15 , it follows from class field theory that the field Q(ζ 15 ) admits no quadratic extension that is unramified outside 3. This contradiction shows that Gal(L/Q(ζ 15 )) is a 3-group, as required.…”

“…Then G and H aré etale over R[ 1 p ] and we can identify them with their Galois modules. The Galois action is unramified outside p. The ring R is a finite product of finite extensions of Z p over which we can apply the theory of Oort-Tate [20], Raynaud [15] and Fontaine [8,9]. Finally, the ring R[ 1 p ] ∼ = F ⊗ Q p is a product of p-adic fields.…”

“…The main result, Proposition 6.3, is used in section 5. See [8,9] The group schemes E are F p 2 -vector space schemes in the sense of Raynaud [15]. The different values for λ correspond to unramified twists.…”

Abelian subvarieties of Drinfeld Jacobians and congruences modulo the characteristic

“…In Proposition 2.3 we will prove a similar (slightly weaker) statement for equicharacteristic R, assuming the abelian varieties in question have toric reduction. We replace the use of Raynaud's theorem [16,Cor. 3.3.6], which is valid only in mixed characteristic, by Lemma 2.1.…”