대수적 수론에서, 대역체(大域體, 영어: global field)는 대수적 수체 및 이와 유사한 함수체를 통틀어 이르는 개념이다.

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  • In de algebraïsche getaltheorie, een deelgebied van de wiskunde, zijn globale velden de centrale objecten van studie. Globale velden veralgemenen lichamen van rationale getallen.Onder een globaal veld worden twee verschillende zaken verstaan:een algebraïsch getallenlichaam, dat wil zeggen een eindige uitbreiding van Q (het veld van de rationale getallen)een globaal funtieveld, dat wil zeggen het functieveld van een algebraïsche kromme over een eindig veld, of op equivalente wijze, een eindige uitbreiding van Fq(T), het veld van de rationale functies in één variabele over het eindige veld met q elementen.
  • 대수적 수론에서, 대역체(大域體, 영어: global field)는 대수적 수체 및 이와 유사한 함수체를 통틀어 이르는 개념이다.
  • In mathematics, the term global field refers to either of the following:an algebraic number field, i.e., a finite extension of Q, ora global function field, i.e., the function field of an algebraic curve over a finite field, equivalently, a finite extension of Fq(T), the field of rational functions in one variable over the finite field with q elements.An axiomatic characterization of these fields via valuation theory was given by Emil Artin and George Whaples in the 1940s.There are a number of formal similarities between the two kinds of fields. A field of either type has the property that all of its completions are locally compact fields (see local fields). Every field of either type can be realized as the field of fractions of a Dedekind domain in which every non-zero ideal is of finite index. In each case, one has the product formula for non-zero elements x:The analogy between the two kinds of fields has been a strong motivating force in algebraic number theory. The idea of an analogy between number fields and Riemann surfaces goes back to Richard Dedekind and Heinrich M. Weber in the nineteenth century. The more strict analogy expressed by the 'global field' idea, in which a Riemann surface's aspect as algebraic curve is mapped to curves defined over a finite field, was built up during the 1930s, culminating in the Riemann hypothesis for curves over finite fields settled by André Weil in 1940. The terminology may be due to Weil, who wrote his Basic Number Theory (1967) in part to work out the parallelism.It is usually easier to work in the function field case and then try to develop parallel techniques on the number field side. The development of Arakelov theory and its exploitation by Gerd Faltings in his proof of the Mordell conjecture is a dramatic example. The analogy was also influential in the development of Iwasawa theory and the Main Conjecture. The proof of the fundamental lemma in the Langlands program also made use techniques which reduced the number field case to the function field case.
  • Globale Körper sind die zentralen Studienobjekte des mathematischen Teilgebietes der algebraischen Zahlentheorie. Sie verallgemeinern den Körper der rationalen Zahlen.
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  • 대수적 수론에서, 대역체(大域體, 영어: global field)는 대수적 수체 및 이와 유사한 함수체를 통틀어 이르는 개념이다.
  • Globale Körper sind die zentralen Studienobjekte des mathematischen Teilgebietes der algebraischen Zahlentheorie. Sie verallgemeinern den Körper der rationalen Zahlen.
  • In mathematics, the term global field refers to either of the following:an algebraic number field, i.e., a finite extension of Q, ora global function field, i.e., the function field of an algebraic curve over a finite field, equivalently, a finite extension of Fq(T), the field of rational functions in one variable over the finite field with q elements.An axiomatic characterization of these fields via valuation theory was given by Emil Artin and George Whaples in the 1940s.There are a number of formal similarities between the two kinds of fields.
  • In de algebraïsche getaltheorie, een deelgebied van de wiskunde, zijn globale velden de centrale objecten van studie.
rdfs:label
  • Corps global
  • Ciało globalne
  • Globaal veld
  • Global field
  • Globaler Körper
  • 대역체
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