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Abelian variety
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Geliefert zwischen Mi., 04.02.2026 und Do., 05.02.2026
Details
In mathematics, particularly in algebraic geometry, complex analysis and number theory, an abelian variety is a projective algebraic variety that is also an algebraic group, i.e., has a group law that can be defined by regular functions. Abelian varieties are at the same time among the most studied objects in algebraic geometry and indispensable tools for much research on other topics in algebraic geometry and number theory. An abelian variety can be defined by equations having coefficients in any field; the variety is then said to be defined over that field. Historically the first abelian varieties to be studied were those defined over the field of complex numbers. Such abelian varieties turn out to be exactly those complex tori that can be embedded into a complex projective space. Abelian varieties defined over algebraic number fields are a special case, which is important also from the viewpoint of number theory. Localisation techniques lead naturally from abelian varieties defined over number fields to ones defined over finite fields and various local fields.
Weitere Informationen
- Allgemeine Informationen
- GTIN 09786130264598
- Editor Frederic P. Miller, Agnes F. Vandome, John McBrewster
- Sprache Englisch
- Größe H220mm x B150mm x T8mm
- Jahr 2009
- EAN 9786130264598
- Format Fachbuch
- ISBN 978-613-0-26459-8
- Titel Abelian variety
- Untertitel Algebraic geometry, Complex analysis, Number theory, Algebraic variety, Algebraic group, Group (mathematics), Regular function, Field (mathematics)
- Gewicht 209g
- Herausgeber Alphascript Publishing
- Anzahl Seiten 128
- Genre Mathematik
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