We consider the structure of rational points on elliptic curves in Weierstrass form. Let x(P ) = AP /B P denote the xcoordinate of the rational point P then we consider when BP can be a prime power. Using Faltings’ Theorem we show that for a fixed power greater than 1, there are only finitely many rational points with this property. Where descent via an isogeny is possible we show, with no rest...

In this paper, we reinterpret the Colmez conjecture on the Faltings height of CM abelian varieties in terms of Hilbert (and Siegel) modular forms. We construct an elliptic modular form involving the Faltings height of a CM abelian surface and arithmetic intersection numbers, and prove that the Colmez conjecture for CM abelian surfaces is equivalent to the cuspidality of this modular form.

In this paper, we reinterpret the Colmez conjecture on Faltings’ height of CM abelian varieties in terms of Hilbert (and Siegel) modular forms. We construct an elliptic modular form involving Faltings’ height of a CM abelian surface and arithmetic intersection numbers, and prove that Colmez’s conjecture for CM abelian surfaces is equivalent to the cuspitality of this modular form.

In this paper, we introduce the notion of co-annihilator of a subsetin a triangle algebra. It is shown that the co-annihilator of asubset is an interval valued residuated lattice (IVRL)-filter. Also, aspecial set of a triangle algebra is defined and the relationshipbetween this set and co-annihilator of a subset in triangle algebrais considered. Finally, co-annihilators preserving congruencerel...

The property that an ideal whose annihilator is zero contains a regular element is examined from the point of view of constructive mathematics. It is shown that this property holds for nitely presented algebras over discrete elds, and for coherent, Noetherian, strongly discrete rings that contain an in nite eld. Let R be a commutative ring and M an R-module. For any subset I of R, we write AM(I...

Let K be an arbitrary field of characteristic not equal to 2. Let m,n ∈ N and V be an m dimensional orthogonal space over K. There is a right action of the Brauer algebra Bn(m) on the n-tensor space V ⊗n which centralizes the left action of the orthogonal group O(V ). Recently G.I. Lehrer and R.B. Zhang defined certain quasiidempotents Ei in Bn(m) (see (1.1)) and proved that the annihilator of ...

Transitioning to a future society, independent of fossil fuels, will definitely require the use of solar radiation for power and fuel production. Due to energy mismatch between device absorption and the broad band irradiation provided by the sun there are severe limitations to how efficient devices for direct conversion of solar radiation can be. One way to better use the solar radiation would ...