Abstract. We show that for any prime number l > 2 the minus class group of the field of the l-th roots of unity Qp(ζl) admits a finite free resolution of length 1 as a module over the ring Ẑ[G]/(1 + ι). Here ι denotes complex conjugation in G = Gal(Qp(ζl)/Qp) ∼= (Z/lZ)∗. Moreover, for the primes l ≤ 509 we show that the minus class group is cyclic as a module over this ring. For these primes we...

Explicit formulae for τ ′ r(L(p, q)) and τ(L(p, q)) are obtained for all L(p, q). There are three systems of invariants of Witten-type for closed oriented 3manifolds: 1. {τr(M), r ≥ 2; τ ′ r(M), r odd ≥ 3}, where τr was defined by Reshetikhin and Turaev [1], and τ ′ r was defined by Kirby-Melvin [2] 2. {Θr(M,A), r ≥ 1,whereA is a 2r-th primitive root of unity} defined by Blanchet, Habegger, Mas...

We replace the group of group-like elements of the quantized enveloping algebra Uq(g) of a finite dimensional semisimple Lie algebra g by some regular monoid and get the weak Hopf algebra w q (g). It is a new subclass of weak Hopf algebras but not Hopf algebras. Then we devote to constructing a basis of w q (g) and determine the group of weak Hopf algebra automorphisms of w q (g) when q is not ...

On the 15th of September 2008, a power-sharing agreement was brokered between the major political parties in Zimbabwe, namely, the Tsvangirai-led Movement for Democratic Change (MDC-T), the Mutambara-led Movement for Democratic Change (MDC-M) and the then ruling Zimbabwe African National Union–Patriotic Front (ZANU-PF). This Global Political Agreement (GPA) paved the way for the establishment o...

ABSTRACT DESSONS, 2006 FLORES, 2013

We show that the height of a nonzero algebraic number α that lies in an abelian extension of the rationals and is not a root of unity must satisfy h(α) > 0.155097.

explanation of the multiplicity of the world and the way it was created from the beginning of existence is one the concerns of philosophers, including mullā ṣadrā. the discourse of the emanation of multiplicity from unity would be totally different with respect to the apparent words of ṣadrā, who believes in the gradational unity of existence and according to his specific viewpoint, believing i...

We construct a canonical compactification SQ g,K of the moduli of abelian varieties over Z[ζN , 1/N ] where ζN is a primitive Nth root of unity. It is very similar to, but slightly different from the compactification SQg,K in [N99]. Any degenerate abelian scheme on the boundary of SQ g,K is one of the (torically) stable quasi-abelian schemes introduced in [AN99], which is reduced and singular. ...