Related papers: Perfectoid spaces arising from arithmetic jet spac…
We determine explicit birational models over Q for the modular surfaces parametrising pairs of N-congruent elliptic curves in all cases where this surface is an elliptic surface. In each case we also determine the rank of the Mordell-Weil…
This survey is a final project of Twopole DRP in fall 20201. In this paper we try to understand a tiny part of the vast theory of perfecoid spaces, called perfectoid fields. We start by giving some motivation and historical background. Then…
Let $X$ be a perfectoid space with tilt $X^\flat$. We construct a canonical map $\theta:\operatorname{Pic} X^\flat\to\lim\operatorname{Pic} X$ where the (inverse) limit is taken over the $p$-power map, and show that $\theta$ is an…
This paper is a subsequent paper of arXiv:2303.07672. We will continue our research on the subject of perfect algebraic spaces that is developed in arXiv:2303.07672. By means of algebraic Frobenius morphisms, we define the perfection of…
This work provides a unified formalism for studying difference and (Hasse-) differential algebraic geometry, by introducing a theory of "iterative Hasse rings and schemes". As an application, Hasse jet spaces are constructed generally,…
The action of origin-preserving diffeomorphisms on a space of jets of symmetric connections is considered. Dimensions of moduli spaces of generic connections are calculated. Poincar\'e series of the geometric structure of symmetric…
We provide necessary and sufficient conditions for when an algebraic stack admits a good moduli space and prove a semistable reduction theorem for points of algebraic stacks equipped with a $\Theta$-stratification. These results provide a…
A perfect Euler cuboid is a rectangular parallelepiped with integer edges and integer face diagonals whose space diagonal is also integer. The problem of finding such parallelepipeds or proving their non-existence is an old unsolved…
The moduli space of jets of certain G-structures (basically those which admit a canonical linear connection) is shown to be isomorphic to the quotient of a natural G-module by G.
Let $A$ be an algebra over an operad in a cocomplete closed symmetric monoidal category. We study the category of $A$-modules. We define certain symmetric product functors of such modules generalising the tensor product of modules over…
We introduce variational approximations for curve evolutions in two-dimensional Riemannian manifolds that are conformally flat, i.e.\ conformally equivalent to the Euclidean space. Examples include the hyperbolic plane, the hyperbolic disk,…
We study jet schemes of Newton non-degenerate plane curve singularities. We identify a subgraph of the graph of jet components and show that it can be constructed from walks on the lattice points in the first quadrant of the Cartesian…
An algebraic scheme is suggested in which discretized spacetime turns out to be a quantum observable. As an example, a toy model producing spacetimes of four points with different topologies is presented. The possibility of incorporating…
It is shown that the groups of automorphisms of Euclidean spaces are isomorphic to the groups of topologic automorphisms of respectively factored arithmetic spaces. In particular, the geometry of Euclidean n-space with positive signature is…
We define an operation of jets on graphs inspired by the corresponding notion in commutative algebra and algebraic geometry. We examine a few graph theoretic properties and invariants of this construction, including chromatic numbers,…
The research project has been made for mathematical modeling of aerospace system Space-to-Surface for avoid intercepting process by flight objects Surface-to-Air. The research has been completed and created mathematical models which used…
The schematic finite spaces are those finite ringed spaces where a theory of quasi-coherent modules can be developed with minimal natural conditions. We give various characterizations of these spaces and their natural morphisms. We show…
The real points of the Deligne-Knudsen-Mumford moduli space of marked points on the sphere has a natural tiling by associahedra. We extend this idea to create a moduli space tiled by cyclohedra. We explore the structure of this space,…
A rational perfect cuboid is a rectangular parallelepiped whose edges and face diagonals are given by rational numbers and whose space diagonal is equal to unity. Finding such a cuboid is equivalent to finding a perfect cuboid with all…
We introduce the notion of tiling spaces for metric spaces. The class of tiling spaces contains the Euclidean spaces, the middle-third Cantor set, and various self-similar spaces appearing in fractal geometry. For doubling tiling spaces, we…