On the good reduction of abelian varieties

Author: gtvx

August undefined, 2024

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 ... WebÉtale Cohomology and Reduction of Abelian Varieties. × Close Log In. Log in with Facebook Log in with Google. or. Email. Password. Remember me on this computer. or …

A note on good reduction of simple Abelian varieties - Semantic …

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 … 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 … small space cabinets kitchen

arXiv:2302.03986v1 [math.NT] 8 Feb 2024

WebGood reduction Johan Commelin March 19, 2013 1 Introduction In a course on elliptic curves the topic of good reduction will pass by sooner or later. ... “Good reduction of abelian varieties”. In: Ann. of Math. (2) 88 (1968), … Web16 de mar. de 2024 · There is a well known theorem by Deuring which gives a criterion for when the reduction of an elliptic curve with complex multiplication (CM) by the ring … highway 3 open bc

Finiteness Theorems for Abelian Varieties over Number Fields

Arithmetik und Geometrie algebraischer Zyklen: Verfahren des …

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 … Web1 de dez. de 2009 · Let A be an abelian variety over a p-adic field K and L an algebraic infinite extension over K.We consider the finiteness of the torsion part of the group of rational points A(L) under some assumptions. In 1975, Hideo Imai proved that such a group is finite if A has good reduction and L is the cyclotomic Z p-extension of K.In this paper, first we … small space ceramic space heaterWebThe abelian varieties of GL 2-type are not absolutely simple in general: they factor up to isogeny as products of varieties defined over number fields.After some work done by Elkies in the one-dimensional case and by Ribet in general, in [pyle] Pyle gives a characterization of the abelian varieties defined over number fields that appear in the absolute … small space chair bed

"WebJSTOR Home " - On the good reduction of abelian varieties

On the good reduction of abelian varieties

On the Order of the Reduction of a Point on an Abelian Variety

WebKey words and phrases. Simple abelian variety, good reduction, p-rank of an abelian variety, Barsotti-Tate group, Dieudonné module, indefinite quaternion algebra, ordinary and supersingu-lar elliptic curves. 'This note is taken from author's Ph. D. thesis, SUNY at Stony Brook, May 1975. The author 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 …

Did you know?

WebBig monodromy theorem for abelian varieties over ﬁnitely generated ﬁelds Sara Arias-de-Reyna Institut fu¨r Experimentelle Mathematik, 45326 Essen, Germany ... Jean-Pierre Serre and J. Tate. Good reduction of abelian varieties. Annals of Mathematics, 88, No. 3:492–517, 1968. [26] Adrian Vasiu. Some cases of the Mumford-Tate conjecture and ... WebAs 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 a fixed rational prime, V the p-adic Tate module of A; and for λ primes of F, ρ λ is the p -adic representation on V of the decomposition group G λ at λ. If ρ ...

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 ... WebSemantic Scholar extracted view of "Abelian varieties having purely additive reduction" by H. Lenstra et al. Skip to search form Skip to main content ... such that if K/Q_p is a …

WebAbstract: Under assumption of the Generalized Riemann Hypothesis we show that every abelian variety over Q(\\sqrt{97}) with good reduction everywhere is isoge... WebABELIAN VARIETIES WITH POTENTIALLY ORDINARY REDUCTION 817 is a P:= P(a) ∈ Q p.Thena is an analytic function of the rigid analytic space associatedtoSpf(I)(inthesenseofBerthelotasin[dJ],Section7). Each (reduced) irreducible component Spec(I) ⊂ Spec(h) has a 2-dimensional absolutely irreducible continuous …

Web23 de jun. de 2004 · Consider a point of infinite order on an abelian variety over a number field. Then its reduction at any place v of good reduction is a torsion point. For most of …

WebAbstract: Under assumption of the Generalized Riemann Hypothesis we show that every abelian variety over Q(\\sqrt{97}) with good reduction everywhere is isoge... small space bathroom wall shelvesWebEntdecke 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! highway 3 openingWeb1 Answer. Sorted by: 4. The answer to (a) is yes. The conductor is given by the representation of an inertia group I v in the Tate module. As T ℓ ( A × B) = T ℓ ( A) × T ℓ ( B), the additivity is easy to see from definition (Serre: Facteurs locaux des fonctions zêta des variétés algébriques, §2. The definition you cite is the same ... highway 3 oregonWeb5 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 . small space chairs wayfairWeb30 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 … small space chair with storageWebOn 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 users and to provide you with a better experience on our websites. small space chair with ottomanWeb11 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 … highway 3 princeton