We study arithmetical and combinatorial properties of β-integers for β being the root of the equation x = mx − n,m, n ∈ N,m ≥ n + 2 ≥ 3. We determine with the accuracy of ±1 the maximal number of β-fractional positions, which may arise as a result of addition of two β-integers. For the infinite word uβ coding distances between consecutive β-integers, we determine precisely also the balance. The...

In this paper we analyse the homotopy type at primes p > 3 of the ring spectrum E`` representing a version of elliptic cohomology whose coefficient ring E``∗ agrees with the ring of modular forms for SL2(Z). For any prime (=maximal) graded ideal P / E``∗ containing the Eisenstein function Ep−1 as well as p, we show that there is a morphism of ring spectra [ E(2) −→ E`` b P and a corresponding s...

1.2. Proposition. — π : PnA → SpecA is a closed morphism. Proof. Suppose Z ↪→ PnA is a closed subset. We wish to show that π(Z) is closed. Suppose y / ∈ π(Z) is a closed point of SpecA. We’ll check that there is a distinguished open neighborhood D(f) of y in SpecA such that D(f) doesn’t meet π(Z). (If we could show this for all points of π(Z), we would be done. But I prefer to concentrate on cl...

In their book Rapoport and Zink constructed rigid analytic period spaces F for Fontaine’s filtered isocrystals and period morphisms from moduli spaces of p-divisible groups to some of these period spaces. They conjectured the existence of an étale bijective morphism F → F of rigid analytic spaces and of interesting local systems of Qp-vector spaces on F. For those period spaces possessing perio...

We prove that any dominant morphism of algebraic varieties over a field k of characteristic zero can be transformed into a toroidal (hence monomial) morphism by projective birational modifications of source and target. This was previously proved by the first and third author when k is algebraically closed. Moreover we show that certain additional requirements can be satisfied.

We prove that any (real or complex) analytic horizontally conformal submersion from a three-dimensional conformal manifold (M, cM ) to a twodimensional conformal manifold (N, cN ) can be, locally, ‘extended’ to a unique harmonic morphism from the H(eaven)-space (H, g) of (M, cN ) to (N, cN ). Moreover, any positive harmonic morphism with two-dimensional fibres from (H, g) is obtained this way.

The main purpose of this paper is to introduce the notion of vague h-morphism on vague graphs and regular vague graphs. The action of vague h-morphism on vague strong regular graphs are studied. Some elegant results on weak and co weak isomorphism are derived. Also, [Formula: see text]-complement of highly irregular vague graphs are defined.

In this paper we introduce the notion of intuitionistic fuzzy f morphism on intutionistic fuzzy graphs and regular intutionistic fuzzy graph. We study the action of intuitionistic fuzzy f morphism on intuitionistic fuzzy strong regular graphs. We derive some simple but elegent results on weak and coweak isomophisms. Mathematics Subject Classification: 03E72, 03F55