Desvl's blog
HomeArchivesCategoriesTagsAbout (Updated Aug. 2022)Link ExchangeSupport the Author
  • Categories
  • Number Theory
Posted 2023-03-20Updated 2023-03-20Number Theory / Algebraic Number Theory / Elementary Number Theory

The Quadratic Reciprocity Law

In this post we deliver the basic computation of the quadratic reciprocity law and see its importance in algebraic number theory.
Read more
Posted 2022-12-23Updated 2022-12-23Number Theory / p-Adic Analysis

The Pontryagin Dual group of Q_p

In this post we show that the Pontryagin dual group of $\mathbb{Q}_p$ is isomorphic to itself.
Read more
Posted 2022-12-20Updated 2022-12-20Number Theory / p-Adic Analysis

The Haar Measure on the Field of p-Adic Numbers

In this post we study the canonical Haar measure on $Q_p$, and give a explicit definition just as the Lebesgue measure.
Read more
Posted 2022-09-04Updated 2022-09-04Algebra / Number Theory / Galois Theory / Algebraic Number Theory

Calculus on Fields - Heights of Polynomials, Mahler's Measure and Northcott's Theorem

We study the height of polynomials and derive some important tools.
Read more
Posted 2022-08-21Updated 2022-12-21Algebra / Commutative Algebra / Number Theory / Algebraic Number Theory / p-adic Analysis / Local Fields

Hensel's Lemma - A Fair Application of Newton's Method and 'Double Induction'

We prove the celebrated Hensel's lemma using the so-called Newton's method and "double induction", and try to find solutions of polynomials in $\mathbb{Q}_p$.
Read more
Posted 2022-07-26Updated 2022-08-26Number Theory / Algebraic Number Theory / Geometry / Algebraic Geometry / Diophantine Geometry

Segre Embedding And Heights

We give a quick look at the Segre embedding and try to use that in a fundamental tool of Diophantine Geometry - heights.
Read more
Posted 2022-06-30Updated 2022-06-30Algebra / Field Theory / Number Theory / Algebraic Number Theory

The Calculus of Fields - Absolute Values

In this post, we develop a fundamental device: absolute value on an arbitrary field with various points of view.
Read more
Desvl

Desvl

A blog mainly on graduate mathematics.

A Noetherian local ring

Posts

90

Categories

47

Tags

54

Follow

Links

  • arXivarxiv.org
  • The Stack Projectstacks.math.columbia.edu
  • nLab (Mathematics)ncatlab.org
  • quiver: a modern commutative diagram editorq.uiver.app
  • The Symmetric Functions Cataloguewww.symmetricfunctions.com
  • Practical Suggestions for Mathematical Speakingwww-math.mit.edu
  • Practical Suggestions for Mathematical Writingwww-math.mit.edu
  • How to study maths really quick (YouTube)www.youtube.com
  • How to study maths really quick (Bilibili)www.bilibili.com
Desvl's blog

© 2023 Desvl
Powered by Hexo & Icarus