Given a normal proper and geometrically connected curve C over the function field K(S) of S, we seek “good” models over S. For instance, if we choose a projective embedding of C into some PK(S) then its Zariski closure in PS is an arithmetic surface (where the S-flatness uses that S is Dedekind). Hence, we can always find an arithmetic surface with generic fiber C. Since S is normal and C is re...

For [contemporary] social anthropologists, the important conclusion, always worth repeating, is that the observation and the labelling of 'behaviour' are inseparable from the importation of socially derived meanings even when observing monkeys. How much more so when the process is reflexive, when the observers and the observed are both 'meaning-makers' ... Edwin Ardener, 1977: Comprehending Oth...

The classical Kummer construction attaches to an abelian surface a K3 surface. As Shioda and Katsura showed, this construction breaks down for supersingular abelian surfaces in characteristic two. Replacing supersingular abelian surfaces by the selfproduct of the rational cuspidal curve, and the sign involution by suitable infinitesimal group scheme actions, I give the correct Kummer-type const...

In America’s visually-oriented, quantitatively illiterate culture, images have a great deal of power, so if a picture is today worth a thousand words, it must be worth a least a billion numbers. This power of the image is a hallmark of the postmodern era, in which the critical role of the observer has come to be recognized, and an understanding of the viewpoint has become inseparable from that ...

We consider the problem of separability: decide whether a Hermitian operator on a finite dimensional Hilbert tensor product H = H ⊗ · · ·⊗H is separable or entangled. We show that the tensor convolution ( φ . . . φ ) : G → H defined for mappings φ : G → H μ on an almost arbitrary locally compact abelian group G, give rise to formulation of an equivalent problem to the separability one.

Separability is one of the most basic and important topological properties. In this paper, separability in (strongly) gyrogroups studied. It proved that every first-countable left ?-narrow strongly gyrogroup separable. Furthermore, it shown if a feathered G isomorphic to subgyrogroup separable gyrogroup, then Therefore, metrizable separable, locally compact

Introduction. The main objects of study in this paper are the commutative separable algebras over a commutative ring. Noncommutative separable algebras have been studied in [2]. Commutative separable algebras have been studied in [1] and in [2], [6] where the main ideas are based on the classical Galois theory of fields. This paper depends heavily on these three papers and the reader should con...