Using arithmetic jet spaces we attach perfectoid to smooth schemes and morphisms of perfectoidspaces $\\delta$-morphisms schemes. We also study attached differential equations defined by some the remarkable appearing in theory such as $\\delta$-charactersof elliptic curves $\\delta$-period maps on modular curves.

In this paper I show that pointwise bounded asymptotic morphisms between separable metrisable locally convex *-algebras induce continuous maps between the quasi-unitary groups of the algebras, provided that the algebras support a certain amount of functional calculus. This links the asymptotic morphisms directly to Thomsen’s non-stable definition of k-theory in the C∗ algebra case. A result on ...

the category whose objects aremorphisms of fine saturated log schemes Y log → X , where Y is a noetherian scheme, and the underlying morphism of schemes Y → X is of finite type, and whose morphisms (from an object Y log 1 → X log to an object Y log 2 → X ) are morphisms of finite type Y log 1 → Y log 2 (i.e., morphisms for which the underlying morphism of schemes Y1 → Y2 is of finite type) lyin...

A word is called primitive if it cannot be expressed as the power of another word. Morphisms preserving primitive words are investigated. Similarly to the word case, each square-free morphism is a primitive morphism but the converse does not hold. A precise characterization of primitive morphisms is provided in terms of pure codes. An easily testable characterization is given for uniform morphi...

We introduce the notion of biextensions of 1-motives by 1-motives and we define morphisms from the tensor product of two 1-motives to a third 1-motive as isomorphism classes of such biextensions. If S is the spectrum of a field of characteristic 0, we check that these biextensions define morphisms from the tensor product of the realizations of two 1-motives to the realization of a third 1-motiv...

Harmonic morphisms are smooth maps between Riemannian manifolds which preserve Laplace's equation. They are characterised as harmonic maps which are horizontally weakly conformal 14, 20]. R.L. Bryant 7] proved that there are precisely two types of harmonic morphisms with one-dimensional bres which can be deened on a constant curvature space of dimension at least four. Here we prove that, on an ...

We show that the class of separable morphisms in the sense of G. Janelidze and W. Tholen in the case of Galois structure of second order coverings of simplicial sets due to R. Brown and G. Janelidze coincides with the class of covering maps of simplicial sets. Introduction Separable morphisms were introduced in [3] by A. Carboni and G. Janelidze for lextensive categories. In the way of [3] one ...