On the good reduction of abelian varieties

Author: gabk

August undefined, 2024

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 … 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 …

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

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. 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 how fast does creeping red fescue spread

Abelian varieties over Q with bad reduction in one prime only

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 ... WebEntdecke 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! 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 … high density and low density

$Abelian varieties over $\mathbb{Q}$ with bad reduction in one …$

ON THE MANIN-MUMFORD CONJECTURE FOR ABELIAN VARIETIES …

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 … WebThe Hecke orbit conjecture asserts that every prime-to- Hecke orbit in a Shimura variety is dense in the central leaf containing it. In this paper, we prove the conjecture for certain … high density altitude meansWeb11 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 … high density altitude takeoff

"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 . " - On the good reduction of abelian varieties

On the good reduction of abelian varieties

LOGARITHMIC GOOD REDUCTION OF ABELIAN VARIETIES

Websupersingular abelian subvariety. Mathematics Subject Classiﬁcation: 14K15 (11R45) Keywords: abelian varieties, rational points, reduction, Galois groups, density … Web1 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 ...

Did you know?

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 … WebOn 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.

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 ... WebJSTOR Home

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 … Web21 de jun. de 2005 · We show that any semi-stable abelian variety over $\mathbb{Q}$ with good reduction outside l = 11 is isogenous to a power of the Jacobian variety of the …

Webhaving “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 …

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 fast does corn growWebÉtale 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 reset password. Enter the email address you signed up with and we'll email you a reset link. Need an account? Click here to sign up. Log In Sign Up. Log In; Sign Up; more; Job ... how fast does cotton growWebA note on good reduction of simple Abelian varieties. C. Adimoolam. Published 1 February 1977. Mathematics. In this note it is shown that the reduction of a simple … high density and crowdingWebAs 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 fast does covid spread in a householdWebIn 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 … high density apartmentWeb7 de mai. de 2012 · We show that there do not exist any non-zero semi-stable abelian varieties over Q with good reduction outside l if and only if l=2, 3, 5, 7 or 13. how fast does costco make glassesWebBig 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 ... high density are inevitable