On number fields with given ramification

Let E be a CM number field and let S be a finite set of primes of E containing the primes dividing a given prime number l and another prime u split above the maximal totally real subfield of E. If ES denotes a maximal algebraic extension of E which is unramified outside S, we show that the natural maps $\mathrm {Gal}(\overline {E_u}/E_u) \longrightarrow \mathrm {Gal}(E_S/E)$ are injective. We discuss generalizations of this result.

Constructions of Non-Commutative Lp-Spaces with a Complex Parameter Arising from Modular Actions

For a von Neumann algebra ℳ and a weight φ on ℳ, we will construct a complex one-parameter family [Formula: see text] of non-commutative Lp-spaces by using Calderón's complex interpolation method. This is a simultaneous and complete extension of the construction of non-commutative Lp-spaces by H. Kosaki and M. Terp. Moreover, we will show that for each p, all the parametrized Lp-spaces are mutually isometrically isomorphic as Banach spaces via natural maps.

An Archaeological Survey of the Tehuacan Valley, Mexico: A Test of Color Infrared Photography

Using data collected by NASA in the Tehuacan Valley, Mexico, tests were undertaken to determine the effectiveness of aerial color infrared film for archaeological reconnaissance. The study area was chosen primarily because MacNeish's Tehuacan Archaeological-Botanical Project (1960-1964) provided a convenient check of site visibility on the photographs, and because microenvironmental zones have been delineated in the valley allowing visibility of sites in different microenvironments to be determined. Our tests indicate that the type of cultural feature or its age are not as important as the environmental situation in distinguishing the site. The greatest archaeological value, however, of color infrared photography is in the delineation of microenvironmental zones and the construction of natural maps rather than the identification of cultural features.

The topological structure of 𝒟–classes

Let S be a compact, topological semigroup with identity. Suppose D, L and R are the D, L and R classes of some x ∈ S. Let (L, α., L/H), (R, β, R/H), (D, γ, D/H) and (D, δ, D/R) by the fibre spaces gotten where α, β γ an δ are the natural maps. It is shown that (D, γ, D/H) has topologically the same structure as the fibre space associated with (L, α, L/H) by R. Also if (L, α, L/H) is locally trivial (locally a cartesian product) then so is (D, δ, D/R) and if both (L, α, L/H) and (R, β, R/H) are locally trivial then so is (D, γ, D/H).

A note on natural maps of higher extension functors

Hilton and Rees have proved (cf. (1), Theorem 1·3) that every natural mapis induced by a map from A to B (or, Hom (A, B) → Next1,1 (A, B) is surjective). It follows that Ext1 (B, −) and Ext1 (A, −) are naturally isomorphic if and only if A and B are quasi-isomorphic (loc. cit., Theorem 2·6), i.e. if there exist projective objects P, Q and an isomorphism . One can ask whether these theorems remain true for higher extension functors.