isogeny


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i·sog·e·nous

 (ī-sŏj′ə-nəs)
adj.
Having the same or similar origin, as organs or parts derived from the same embryonic tissue.

i·sog′e·ny n.

isogenesis, isogeny

the state or process of deriving from the same source or origins, as different parts deriving from the same embryo tissues. — isogenic, isogenetic, adj.
See also: Origins
References in periodicals archive ?
Here [[??].sub.i] are the base change maps; [??] is induced from the natural [alpha]-action on the bundle [C.sup.2] and gives an isogeny of degree det([alpha]) at each smooth fibre.
On the other hand, under [Laplace] [equivalent] [??]]K [K.sub.[??]], the pullback of weight 1 modular forms agrees with the det [([alpha]).sup.-1] multiple of the pullback of 1-forms on the fibres by the isogeny [alpha] : [S.sub.[[omega]]] [right arrow] [S.sub.[[omega][alpha]]], because [alpha] multiplies the symplectic form by det([alpha]).
Our characterization of the Igusa curves will depend on the isogeny invariance of the p-adic Galois character associated to an elliptic curve in characteristic p.
Specifically, [w.sub.N] maps the triple [mathematical Expressions Omitted] onto [Mathematical Expressions Omitted], where [Mathematical Expressions Omitted] is the isogeny which is dual to [phi].
Since [rho] : [D.sub.[xi] right arrow] [D'.sub.[xi]] is an isogeny, if I'((D) is defined as in the remark after Theorem 3, then the absolute convergence of I'([phi]) for every [phi] in S([X.sub.A]) there is invariant under strong equivalence relation and castling transforms.
In this paper we shall study from the "differential algebraic viewpoint" the moduli spaces [A.sub.g,n] of principally polarized abelian F-varieties with level n structure; we will be especially concerned with understanding from this viewpoint the isogeny equivalence relation on [A.sub.g,n].
So we are provided with an equivalence relation on F called isogeny.
The Isogeny Theorem due to Faltings ([4], [section]5 Korollar 2) implies that
Then the Isogeny Theorem implies that [V.sub.l](E) and[V.sub.l](E') are isomorphic as [G.sub.F]'-modules for any prime '.
Let [Y.sup.0] [subset] Y be a neighbourhood of [t.sub.0] on which the isogeny [B.sub.t0] [right arrow] [B.sub.t0]/[H.sub.t0] can be extended to an isogeny:
[MATHEMATICAL EXPRESSION OMITTED] and by [[psi].sub.y] [[psi].sub.y]; = [rho] [omicron] [[phi].sub.y] (3.2) the composition with an isogeny [rho] in such a way that [A.sub.y] := [rho]([A'.sub.y]) is principally polarized (cf.
Ono [12,17] whose study of the behavior of [tau] under an isogeny explains the presence of Pic(H), and reduces the semisimple case to the simply connected case.