For any finite volume hyperbolic 3-manifold M we use ideal triangulation to define an invariant β(M) in the Bloch group B(C ). It actually lies in the subgroup of B(C ) determined by the invariant trace field of M . The Chern-Simons invariant of M is determined modulo rationals by β(M). This implies rationality and — assuming the Ramakrishnan conjecture — irrationality results for Chern Simons ...

It is well known to generalize the meagre ideal replacing ℵ 0 by a (regular) cardinal λ > ℵ 0 and requiring the ideal to be λ +-complete. But can we generalize the null ideal? In terms of forcing, this means finding a forcing notion similar to the random real forcing, replacing ℵ 0 by λ, so requiring it to be (< λ)-complete. Of course, we would welcome additional properties generalizing the one...

Let A = Fq [T ] be the ring of polynomials over the finite field Fq and 0 = a ∈ A. Let C be the A-Carlitz module. For a monic polynomial m ∈ A, let C(A/mA) and ā be the reductions of C and a modulo mA respectively. Let fa(m) be the monic generator of the ideal {f ∈ A,Cf (ā) = 0̄} on C(A/mA). We denote by ω(fa(m)) the number of distinct monic irreducible factors of fa(m). If q = 2 or q = 2 and a ...

We prove a commutative algebra result which has consequences for congruences between automorphic forms modulo prime powers. If C denotes the congruence module for a fixed automorphic Hecke eigenform π0 we prove an exact relation between the p-adic valuation of the order of C and the sum of the exponents of p-power congruences between the Hecke eigenvalues of π0 and other automorphic forms. We a...

For a finite dimensional monomial algebra Λ over a field K we show that the Hochschild cohomology ring of Λ modulo the ideal generated by homogeneous nilpotent elements is a commutative finitely generated Kalgebra of Krull dimension at most one. This was conjectured to be true for any finite dimensional algebra over a field in [13].

In this paper we prove some results on combinatorics of triangulations of 3-dimensional pseudo-manifolds, improving on results of [NZ], and apply them to obtain a simplicial formula for the Chern-Simons invariant of an ideally triangulated hyperbolic 3-manifold. Combining this with [MN] gives a simplicial formula for the η invariant also. In effect, the main ingredient in the formula is the sum...

We show the existence of a subalgebra A ⊆ P(ω) that satisfies the following three conditions: • A is Borel (when P(ω) is identified with 2). • A is arithmetically closed (i.e., A is closed under the Turing jump, and Turing reducibility). • The forcing notion (A,⊆) modulo the ideal FIN of finite sets collapses the continuum to א0.

let $a$ be an arbitrary banach algebra and $varphi$ a homomorphism from $a$ onto $bbb c$. our first purpose in this paper is to give some equivalent conditions under which guarantees a $varphi$-mean of norm one. then we find some conditions under which there exists a $varphi$-mean in the weak$^*$ cluster of ${ain a; |a|=varphi(a)=1}$ in $a^{**}$.