Related papers: Adic Spaces

These informal notes were prepared in connection with a lecture at a high school mathematics tournament, and provide an overview of some examples of metric spaces and a few of their basic properties.

In these informal lecture notes we outline different approaches used in doing calculations involving the Dirac equation in curved spacetime. We have tried to clarify the subject by carefully pointing out the various conventions used and by…

Here I share a few notes I used in various course lectures, talks, etc. Some may be just calculations that in the textbooks are more complicated, scattered, or less specific; others may be simple observations I found useful or curious.

These informal notes deal with some basic properties of metric spaces, especially concerning lengths of curves.

These are some informal notes concerning topological vector spaces, with a brief overview of background material and basic notions, and emphasis on examples related to classical analysis.

This note is a survey of $J$-spaces.

These notes give an elementary approach to parts of the theory of standard Borel and analytic spaces.

These are the notes from my courses on the arithmetic of quadratic forms.

These notes deal with some basic notions related to p-adic numbers and functions of p-adic numbers.

These informal notes are concerned with sums and averages in various situations in analysis.

These informal notes are concerned with spaces of functions in various situations, including continuous functions on topological spaces, holomorphic functions of one or more complex variables, and so on.

These are notes from a lecture course on symmetric spaces by the second author given at the University of Pittsburgh in the fall of 2010.

I provide some comments on Arithmetic Teichmuller Spaces constructed in my paper arXiv:2106.11452.

The notes provide a short introduction to de Branges--Rovnyak spaces. They cover some basic facts and are intended to give the reader a taste of the theory, providing sufficient motivation to make it interesting.

Quoted speech is often set off by punctuation marks, in particular quotation marks. Thus, it might seem that the quotation marks would be extremely useful in identifying these structures in texts. Unfortunately, the situation is not quite…

These notes include introductory material on the notion of splitting fields for modules over a k-algebra where k is a field.

These are extended notes of the course given by the author at RIMS, Kyoto, in October 2016. The aim is to give a self-contained overview on the recently developed approach to differential calculus on metric measure spaces. The effort is…

These informal notes are an expanded version of lectures on the moduli space of elliptic curves given at Zhejiang University in July, 2008. Their goal is to introduce and motivate basic concepts and constructions (such as orbifolds and…

The objective of this paper is to explain the principles of the design of a coarse space in a simplified way and by pictures. The focus is on ideas rather than on a more historically complete presentation. Also, space limitation does not…

A generalization of metric space is presented which is shown to admit a theory strongly related to that of ordinary metric spaces. To avoid the topological effects related to dropping any of the axioms of metric space, first a new, and…