On the good reduction of abelian varieties
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 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 ... WebAbstract: Under assumption of the Generalized Riemann Hypothesis we show that every abelian variety over Q(\\sqrt{97}) with good reduction everywhere is isoge...
On the good reduction of abelian varieties
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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 ... 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 ...
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. Web18 de fev. de 2004 · Let K be a number field and A an abelian variety over K. We are interested in the following conjecture of Morita: if the Mumford-Tate group of A does not contain unipotent ℚ-rational points then A has potentially good reduction at any discrete place of K. The Mumford-Tate group is an object of analytical nature whereas having …
WebWe study semistable reduction and torsion points of abelian varieties. In particular, we give necessary and sufficient conditions for an abelian variety to have semistable reduction. We also study Néron models of abelian varieties with potentially good reduction and torsion points of small order. We study some invariants that measure the … Websupersingular abelian subvariety. Mathematics Subject Classification: 14K15 (11R45) Keywords: abelian varieties, rational points, reduction, Galois groups, density …
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.
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 ... dutch angle camera angleWebOn 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. dvd star trek picard season 2 amazonWeban 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) dvd stanley tucci searching for italyWeb11 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 … dutch angle filmWebAn 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 … dvd stealthWebRecall 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 dvd state of playWebThe 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 … dvd step brothers