Differential Galois theory

간단한 소개

How important is the transitivity in Galois theory and Monodromy theory?

 

meaning of transitivity = 

 

 

dictionary

geometric viewpoints vs field theoretic viewpoints (or algebra vs. geometry)

covering space - field extensions

regular covering - Galois covering

degree of covering - degree of field extension

Spec of ring of integers - number fields

Riemann surfaces or algebraic curve - function field

 

example

\(x^3-2=0\)

\(K=\mathbb{Q}(\omega, \sqrt[3]{2})\) over \(\mathbb{Q}\)

\(Spec \mathbb{Z}[\omega,\sqrt[3]2]\) over \(Spec \mathbb{Z}\)

\([K : \mathbb{Q}]=6\)

Note that this degree is not equal to the degree of the polynomial.

 

 

 

 

 

 

하위페이지

• 갈루아 이론
  
  • Abel's impossibility theorem
    
  • adele and idele
    
  • algebraic functions
    
  • Class Field Theory
    
  • Differential Galois theory
    
  • Liouville theory
    
  • number fields and threefolds
    
  • 고전적인 갈루아 이론
    
  • 대수적정수론
    

 

 

 

 

 

 

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관련된 다른 주제들

작도문제

• 가우스와 정17각형의 작도
  
• 그리스 3대 작도 불가능문제
  
  • 두배의 부피를 갖는 정육면체(The duplication of the cube)
    
• 정다각형의 작도
  
• 히포크라테스의 초승달
  

 

표준적인 도서 및 추천도서

• http://gigapedia.info/1/galois_theory
• http://gigapedia.info/1/
• http://gigapedia.info/1/
• http://gigapedia.info/1/
• http://gigapedia.info/1/
• http://www.amazon.com/s/ref=nb_ss_gw?url=search-alias%3Dstripbooks&field-keywords=

 

 

참고할만한 자료

• http://ko.wikipedia.org/wiki/
• http://en.wikipedia.org/wiki/
• http://front.math.ucdavis.edu/search?a=&t=&c=&n=40&s=Listings&q=
• http://www.ams.org/mathscinet/search/publications.html?pg4=AUCN&s4=&co4=AND&pg5=TI&s5=&co5=AND&pg6=PC&s6=&co6=AND&pg7=ALLF&co7=AND&Submit=Search&dr=all&yrop=eq&arg3=&yearRangeFirst=&yearRangeSecond=&pg8=ET&s8=All&s7=
• 다음백과사전 http://enc.daum.net/dic100/search.do?q=

 

 

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