On the good reduction of abelian varieties

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Web5 de set. de 2024 · Corollary 1.3 thus generalizes the main result of [11], which treats the case where G is the base change to O K of a good reduction abelian variety over a finite unramified extension of Q p . WebIn this paper we study the reduction of abelian varieties. In particular, we study the relationships between n-torsion points onXand the reduction of X, where X is an abelian …

On p -adic uniformization of abelian varieties with good reduction

Web2 de out. de 2024 · We show that up to potential isogeny, there are only finitely many abelian varieties of dimension d defined over a number field K, such that for any finite place v outside a fixed finite set S of places of K containing the archimedean places, it has either good reduction at v, or totally bad reduction at v and good reduction over a quadratic … Web11 de fev. de 2024 · In this case X → A is an isogeny and it follows from Neron-Ogg-Shafarevich that X has good reduction as well over R. Thus, X has potential good reduction over R, i.e., there is a finite extension L / K such that X R L has a smooth proper model over R L, where R L is the integral closure of R in L. I fear that my answer has a … how do i choose a retirement plan

[alg-geom/9602014] Reduction of abelian varieties - arXiv.org

WebRecall that an abelian variety over a complete ﬁeld K is said to have potentially good reductionif there exists a ﬁnite ﬁeld extensionL/K such that the base change of A to L is the generic ﬁber of an abelian scheme over the valuation ring of L. If R is any Dedekind domain with quotient ﬁeld K, we will say that an abelian variety A/K WebAn abelian variety with sufficiently many complex multiplications has potentially good reduction; in case the residue class field is finite this was proved by Serre and Tate; in … WebSerre, J.-P., Tate, J.: Good reduction of Abelian varieties. Ann. Math.68, 492–517 (1968) Google Scholar Tate, J.: Algorithm for determining the type of a singular fiber in an elliptic pencil. In: Modular functions in one variable IV. Lecture Notes in ... how do i choose a printer

$René Schoof: Abelian varieties over Q(\sqrt{97}) with good reduction ...$

Abelian varieties over Q with bad reduction in one prime only

Webabelian variety over the ﬁnite ﬁeld F q is a Weil q-number, see Theorem 3.2. We will see that A∼B ⇒ π A∼π B, i.e. abelian varieties deﬁned over the same ﬁnite ﬁeld Kisogenous over Kdeﬁne conjugated Weil numbers. We will write {simple abelian variety over K}/∼ K =: M(K,s) for the set of isogeny classes of simple abelian ... Web7 de dez. de 2011 · Abstract. We show that there are no non-zero semi-stable abelian varieties over { {\bf Q} (\sqrt {5})} with good reduction outside 3 and we show that the only semi-stable abelian varieties over Q with good reduction outside 15 are, up to isogeny over Q, powers of the Jacobian of the modular curve X 0 (15). Download to read the full … how do i choose a medicare part d planWebEntdecke Arithmetik und Geometrie algebraischer Zyklen: Verfahren des NATO-Fortschritts in großer Auswahl Vergleichen Angebote und Preise Online kaufen bei eBay Kostenlose Lieferung für viele Artikel! how do i choose a safe vitamin brand

"Web2 de out. de 2024 · Then its reduction at any place v of good reduction is a torsion point. For most of this paper we fix a rational prime and study how the -part of this reduction … " - On the good reduction of abelian varieties

On the good reduction of abelian varieties

[alg-geom/9602014] Reduction of abelian varieties - arXiv.org

Web30 de abr. de 1976 · In this paper we prove that there does not exist a two-dimensional abelian variety defined over Q and having everywhere good reduction. Bibliography: 3 … WebThen there are only finitely many isomorphism classes of abelian varieties over K with polarizations of degree d which have good reduction outside of S. Keywords. Line Bundle; Prime Number; Isomorphism Class; Abelian Variety; Finiteness Theorem; These keywords were added by machine and not by the authors.

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Web19 de fev. de 1996 · We study semistable reduction and torsion points of abelian varieties. In particular, we give necessary and sufficient conditions for an abelian variety to have … Weban imaginary quadratic ﬁeld K with a prime of bad reduction greater than 6 has a surjective mod p Galois representation. The bound on p depends on K and the degree of the isogeny ... one wonders whether modular abelian varieties can address the classical problem of describing all solutions to the generalized Fermat equation Ap +Bq = Cr (1.1)

Webabelian varieties, either both have, or both have not, good reduction at v. Indeed, f maps T,(A) onto a subgroup of finite index of T,(A') and, if I(vj) acts trivially on the former, it … WebAbstract: Under assumption of the Generalized Riemann Hypothesis we show that every abelian variety over Q(\\sqrt{97}) with good reduction everywhere is isoge...

WebIn 1929, Weil [17] generalized the Mordell’s theorem to all abelian varieties over number ﬁelds. And then, Faltings [5] proved the Mordell’s conjecture in 1983. But Falting’s proof is not effective. ... Weil rank r2r+2. Denote by Cthe reduction of Cmodulo p. Then (2) #C(Q)≤#C(F WebJacobian varieties J0(l2) of the modular curves X0(l2) are other examples of abelian vari- eties over Q that have good reduction at all primes diﬀerent from l. These abelian varieties are not semi-stable at l. However, S.J. Edixhoven [5] showed that J0(l2) acquires semi- stable reduction at l over an extension that is merely tamely ramiﬁed at l.

WebTorp(A)∩ X is Zariski dense in X,thenX is a translate of an abelian subvariety of A, that is, X = A +a,whereA is an abelian subvariety of A and a ∈ A. Proof. Let A F be the reduction of A at v, which is a supersingular abelian va-riety over F.Letq be the cardinality of F,whichisapowerofp.Letσ ∈ Gal(F/F)betheq-th power Frobenius ...

WebOn p-adic uniformization of abelian varieties with good reduction We present a proof, whose sketch was supplied by Pierre Colmez, that if T p(A)GK = 0, then Fontaine’s … how much is neutering a male cat ukWebOur second result concerns abelian varieties over Q that have good reduction outside l and acquire semi-stable reduction at l over a tamely ramiﬁed extension. Theorem 1.3. For the primesl =2,3 or 5, there do not exist any non-zero abelian varieties over Q that have good reduction at every prime diﬀerent from l and acquire semi-stable ... how much is neutering a cat in philippinesWebAs the reduction behavior is determined by the Galois representations of the decompositon groups, one can reformulate the problem as follows: let A be an abelian variety over F, p … how do i choose a mobile phone how much is neuschwanstein castle worthWebSerre, J.-P., Tate, J.: Good reduction of Abelian varieties. Ann. Math.68, 492–517 (1968) Google Scholar Tate, J.: Algorithm for determining the type of a singular fiber in an … how do i choose a tens unitWebOn p-adic uniformization of abelian varieties with good reduction - Volume 158 Issue 7. Skip to main content Accessibility help We use cookies to distinguish you from other … how do i choose a steel column sizeWebhaving “logarithmic good reduction”. Such a formula had been proven for cohomologically tame semi-abelian varieties by Halle–Nicaise [4, §8.1]. Hence Theorem 1.2 shows that … how much is neutering a male cat