An Introduction to Imaginary Geometry

نویسندگان

  • Mark Sellke
  • Andrew Ahn
  • Scott Sheffield
چکیده

This expository paper is based on the theory of imaginary geometry, due to Sheffield and Miller. We aim to explain enough of the theory for the reader to understand the main constructions and some basic interactions between them in a short time. We suppress the more technical aspects when possible to focus attention on building geometric intuition.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Discrete Differential Geometry: an Applied Introduction

domain M parameterization immersed surface Remember that, like the cartographers of yore, our goal is to parameterize a given surface over the plane. In particular, we want to find a map that preserves angles. How can we express this condition more explicitly? Well, we know how to express 90-degree rotations on the surface, using the complex structure J . And we know how to express 90-degree ro...

متن کامل

Noncommutative Geometry and Arithmetic

This is an overview of recent results aimed at developing a geometry of noncommutative tori with real multiplication, with the purpose of providing a parallel, for real quadratic fields, of the classical theory of elliptic curves with complex multiplication for imaginary quadratic fields. This talk concentrates on two main aspects: the relation of Stark numbers to the geometry of noncommutative...

متن کامل

On the curious historical coincidence of algebra and double-entry bookkeeping

The emergence of symbolic algebra is probably the most important methodological innovation in mathematics since the Euclidean axiomatic method in geometry. Symbolic algebra accomplished much more than the introduction of symbols in mathematics. It allowed for the abstraction and generalization of the concepts of number, quantity and magnitude. It led to the acceptance of negative numbers and im...

متن کامل

The Unit Group of a Real Quadratic Field

While the unit group of an imaginary quadratic field is very simple, the unit group of a real quadratic field has nontrivial structure. Its study involves some geometry and analysis, but also it relates to Pell's equation and continued fractions, topics from elementary number theory.

متن کامل

The Fate of One Forgotten Idea: N.a.vasiliev and His Imaginary Logic

The fate of logical ideas is whimsical. Very often time only gives us the opportunity to appraise the strength of forecasting of the scholar, the scale of his ideas, their orientation to the future, and the role and place of the scholar in the intellectual history of mankind. ''Time has a difficult delivery, but never a miscarriage''-as one aphorism put it. Today, the significance of the logica...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2016