On the good reduction of abelian varieties
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 … WebAuthor: Haruzo Hida Publisher: Springer Science & Business Media ISBN: 1468493906 Category : Mathematics Languages : en Pages : 390 Download Book. Book Description In the early years of the 1980s, while I was visiting the Institute for Ad vanced Study (lAS) at Princeton as a postdoctoral member, I got a fascinating view, studying congruence …
On the good reduction of abelian varieties
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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 ... 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 …
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 … 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 ...
WebAbstract: Under assumption of the Generalized Riemann Hypothesis we show that every abelian variety over Q(\\sqrt{97}) with good reduction everywhere is isoge... 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 …
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
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 small manicure kitWebAs 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 … small mango wood side tableWeb21 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 … small manicure set for menWebABELIAN 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 … son moto harleysonm short interestWebJSTOR Home son moving awayWeban 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) small mango tree not growing