Conjectures in Arithmetic Algebraic Geometry: A Survey
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Wiesbaden
Vieweg+Teubner Verlag
1994
|
| Ausgabe: | Second Revised Edition |
| Schriftenreihe: | Aspects of Mathematics : E
18 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | In this expository text we sketch some interrelations between several famous conjectures in number theory and algebraic geometry that have intrigued mathematicians for a long period of time. Starting from Fermat's Last Theorem one is naturally led to introduce Lfunctions, the main, motivation being the calculation of class numbers. In particular, Kummer showed that the class numbers of cyclotomic fields play a decisive role in the corroboration of Fermat's Last Theorem for a large class of exponents. Before Kummer, Dirichlet had already successfully applied his L-functions to the proof of the theorem on arithmetic progressions. Another prominent appearance of an L-function is Riemann's paper where the now famous Riemann Hypothesis was stated. In short, nineteenth century number theory showed that much, if not all, of number theory is reflected by properties of L-functions. Twentieth century number theory, class field theory and algebraic geometry only strengthen the nineteenth century number theorists's view. We just mention the work of E. H~cke, E. Artin, A. Weil and A. Grothendieck with his collaborators. Heeke generalized Dirichlet's L-functions to obtain results on the distribution of primes in number fields. Artin introduced his L-functions as a non-abelian generalization of Dirichlet's L-functions with a generalization of class field theory to non-abelian Galois extensions of number fields in mind |
| Beschreibung: | 1 Online-Ressource (VII, 246 p) |
| ISBN: | 9783663095057 9783663095071 |
| ISSN: | 0179-2156 |
| DOI: | 10.1007/978-3-663-09505-7 |
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Datensatz im Suchindex
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| author | Hulsbergen, Wilfred W. J. |
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| discipline | Mathematik |
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| illustrated | Not Illustrated |
| indexdate | 2024-12-03T09:00:54Z |
| institution | BVB |
| isbn | 9783663095057 9783663095071 |
| issn | 0179-2156 |
| language | English |
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| spelling | Hulsbergen, Wilfred W. J. Verfasser aut Conjectures in Arithmetic Algebraic Geometry A Survey by Wilfred W. J. Hulsbergen Second Revised Edition Wiesbaden Vieweg+Teubner Verlag 1994 1 Online-Ressource (VII, 246 p) txt rdacontent c rdamedia cr rdacarrier Aspects of Mathematics : E 18 0179-2156 In this expository text we sketch some interrelations between several famous conjectures in number theory and algebraic geometry that have intrigued mathematicians for a long period of time. Starting from Fermat's Last Theorem one is naturally led to introduce Lfunctions, the main, motivation being the calculation of class numbers. In particular, Kummer showed that the class numbers of cyclotomic fields play a decisive role in the corroboration of Fermat's Last Theorem for a large class of exponents. Before Kummer, Dirichlet had already successfully applied his L-functions to the proof of the theorem on arithmetic progressions. Another prominent appearance of an L-function is Riemann's paper where the now famous Riemann Hypothesis was stated. In short, nineteenth century number theory showed that much, if not all, of number theory is reflected by properties of L-functions. Twentieth century number theory, class field theory and algebraic geometry only strengthen the nineteenth century number theorists's view. We just mention the work of E. H~cke, E. Artin, A. Weil and A. Grothendieck with his collaborators. Heeke generalized Dirichlet's L-functions to obtain results on the distribution of primes in number fields. Artin introduced his L-functions as a non-abelian generalization of Dirichlet's L-functions with a generalization of class field theory to non-abelian Galois extensions of number fields in mind Engineering Engineering, general Ingenieurwissenschaften Vermutung (DE-588)4117354-5 gnd rswk-swf Zahlentheorie (DE-588)4067277-3 gnd rswk-swf Beilinson-Vermutung (DE-588)4211642-9 gnd rswk-swf Algebraische Geometrie (DE-588)4001161-6 gnd rswk-swf L-Funktion (DE-588)4137026-0 gnd rswk-swf Algebraische Geometrie (DE-588)4001161-6 s Zahlentheorie (DE-588)4067277-3 s Vermutung (DE-588)4117354-5 s 1\p DE-604 L-Funktion (DE-588)4137026-0 s 2\p DE-604 Beilinson-Vermutung (DE-588)4211642-9 s 3\p DE-604 Aspects of Mathematics E 18 (DE-604)BV000018737 18 https://doi.org/10.1007/978-3-663-09505-7 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Hulsbergen, Wilfred W. J. Conjectures in Arithmetic Algebraic Geometry A Survey Engineering Engineering, general Ingenieurwissenschaften Vermutung (DE-588)4117354-5 gnd Zahlentheorie (DE-588)4067277-3 gnd Beilinson-Vermutung (DE-588)4211642-9 gnd Algebraische Geometrie (DE-588)4001161-6 gnd L-Funktion (DE-588)4137026-0 gnd |
| subject_GND | (DE-588)4117354-5 (DE-588)4067277-3 (DE-588)4211642-9 (DE-588)4001161-6 (DE-588)4137026-0 |
| title | Conjectures in Arithmetic Algebraic Geometry A Survey |
| title_auth | Conjectures in Arithmetic Algebraic Geometry A Survey |
| title_exact_search | Conjectures in Arithmetic Algebraic Geometry A Survey |
| title_full | Conjectures in Arithmetic Algebraic Geometry A Survey by Wilfred W. J. Hulsbergen |
| title_fullStr | Conjectures in Arithmetic Algebraic Geometry A Survey by Wilfred W. J. Hulsbergen |
| title_full_unstemmed | Conjectures in Arithmetic Algebraic Geometry A Survey by Wilfred W. J. Hulsbergen |
| title_short | Conjectures in Arithmetic Algebraic Geometry |
| title_sort | conjectures in arithmetic algebraic geometry a survey |
| title_sub | A Survey |
| topic | Engineering Engineering, general Ingenieurwissenschaften Vermutung (DE-588)4117354-5 gnd Zahlentheorie (DE-588)4067277-3 gnd Beilinson-Vermutung (DE-588)4211642-9 gnd Algebraische Geometrie (DE-588)4001161-6 gnd L-Funktion (DE-588)4137026-0 gnd |
| topic_facet | Engineering Engineering, general Ingenieurwissenschaften Vermutung Zahlentheorie Beilinson-Vermutung Algebraische Geometrie L-Funktion |
| url | https://doi.org/10.1007/978-3-663-09505-7 |
| volume_link | (DE-604)BV000018737 |
| work_keys_str_mv | AT hulsbergenwilfredwj conjecturesinarithmeticalgebraicgeometryasurvey |