Related papers: Smooth scheme morphisms: a fresh view
For a smooth proper scheme or formal scheme over an unramified, complete DVR of mixed characteristics we prove a comparison isomorphism relating etale cohomology of the generic fiber with values in a crystalline etale sheaf to the…
In this paper we study flatness of the restriction on some special subgerms (e.g. the reduction and the unmixed part) of the total space of a flat morphism over a smooth base space. We give a relationship between reducedness of the total…
We introduce and study configuration schemes, which are obtained by ``glueing'' usual schemes along closed embeddings. The category of coherent sheaves on a configuration scheme is investigated. Smooth configuration schemes provide…
We revisit the notion of one-sided recognizability of morphisms and its relation to two-sided recognizability.
Dynamical quantum field theories (QFTs), such as those in which spacetimes are equipped with a metric and/or a field in the form of a smooth map to a target manifold, can be formulated axiomatically using the language of…
In this paper we discuss different properties of noncommutative schemes over a field. We define a noncommutative scheme as a differential graded category of a special type. We study regularity, smoothness and properness for noncommutative…
Many innovative applications require establishing correspondences among 3D geometric objects. However, the countless possible deformations of smooth surfaces make shape matching a challenging task. Finding an embedding to represent the…
Variational analysis presents a unified theory encompassing in particular both smoothness and convexity. In a Euclidean space, convex sets and smooth manifolds both have straightforward local geometry. However, in the most basic hybrid case…
Flatness of discrete-time systems can be characterized by two simple properties. There exists a map, a submersion, from the flat coordinates and their forward shifts to the state and the input of the discrete-time system, such that the…
An isomorphism of symplectically tame smooth pseudocomplex structures on the complex projective plane which is a homeomorphism and differentiable of full rank at two points is smooth.
The paper develops a novel analysis of mutual interactions between topology and soft topology. It is known that each soft topology produces a system of crisp (parameterized) topologies. The other way round is also possible. Namely, one can…
We generalize the functorial quasi-isomorphism in \cite{Davis2011} from overconvergent Witt de-Rham cohomology to rigid cohomology on smooth varieties over a finite field $k$, dropping the quasi-projectiveness condition. We do so by…
Divided into three parts, the first marks out enormous geometric issues with the notion of quasi-freenss of an algebra and seeks to replace this notion of formal smoothness with an approximation by means of a minimal unital commutative…
We introduce a notion of proper morphism for schematic finite spaces and prove the analogue of Grothendieck's finiteness theorem for it by means of the classic result for schemes and general descent arguments. This result also generalizes…
We show that for flat morphisms between varieties with rational singularities, the higher direct images of the structure sheaf are locally free. As a consequence, the identity component of the relative Picard scheme is a smooth algebraic…
In this paper we introduce congruence spaces, which are topological spaces that are canonically attached to monoid schemes and that reflect closed topological properties. This leads to satisfactory topological characterizations of closed…
For a general $k$-gonal curve $C$ with a morphism $f: C \rightarrow \mathbb{P}^1$ of degree $k$, we consider the refinement of the Brill-Noether schemes $W^r_d(C)$ by means of the Brill-Noether degeneracy schemes…
We study two classes of morphisms in infinite type: tamely presented morphisms and morphisms with coherent pullback. These are generalizations of finitely presented morphisms and morphisms of finite Tor-dimension, respectively. The class of…
We aim at giving a rigorous proof of the state-ments on the smoothness and the dimension of Severi varieties wherethere are gaps in the proofs in some standard literature. The method isa mixture of algebraic and analytic methods.
Let $u:A\to B$ be a morphism of noetherian local rings. We obtain smoothness criteria for algebras with differential bases, in the case of rings containing a field of characteristic $p>0.$ We also give smoothness criteria for reduced…