Geometric methods in algebra and number theory
The transparency and power of geometric constructions has been a source of inspiration for generationsof mathematicians. Their applications to problems in algebraandnumber theory goback to Diophantus,if not earlier. Naturally, the Greek techniques of intersecting lines and conics have given way to m...
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| Main Author: | |
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| Other Authors: | , , |
| Format: | Livre numérique |
| Language: | Anglais |
| Published: |
Boston, MA :
Birkhäuser Boston
[20..].
Cham : Springer Nature |
| Edition: | 1st ed. 2005. |
| Series: | Progress in Mathematics
235 |
| Online Access: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Note: |
Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Geometric methods in algebra and number theory, Fedor Bogomolov, Yuri Tschinkel, editors, Boston, Birkhäuser, 2005, 1 vol. (VIII-362 p.), Progress in mathematics, 0-8176-4349-4 • Geometric Methods in Algebra and Number Theory, Texte imprimé, 9780817670733 • Geometric methods in algebra and number theory, Fedor Bogomolov, Yuri Tschinkel, editors, Boston, Birkhäuser, 2005, 1 vol. (VIII-362 p.), Progress in mathematics, 0-8176-4349-4 |
| Summary: | The transparency and power of geometric constructions has been a source of inspiration for generationsof mathematicians. Their applications to problems in algebraandnumber theory goback to Diophantus,if not earlier. Naturally, the Greek techniques of intersecting lines and conics have given way to much more sophisticated and subtle constructions. What remains unchallenged is the beauty and persuasion of pictures, communicated in words or drawings. Thisvolumecontainsaselectionofarticlesexploringgeometricapproaches to problems in algebra,algebraicgeometryand number theory. All papers are strongly in?uenced by geometric ideas and intuition. Several papers focus on algebraic curves: the themes range from the study of unrami?ed curve c- ers (Bogomolov Tschinkel), Jacobians of curves (Zarhin), moduli spaces of curves (Hassett) to modern problems inspired by physics (Hausel). The - per by Bogomolov Tschinkelexplores certain special aspects of the geometry of curves over number ?elds: there exist many more nontrivial corresp- dences between such curves than between curves de?ned over larger ?elds. Zarhin studies the structure of Jacobians of cyclic covers of the projective line and provides an e?ective criterion for this Jacobian to be su?ciently generic. Hassett applies the logarithmic minimal model program to moduli spaces of curves and describes it in complete detail in genus two. Hausel st- ies Hodge-type polynomials for mixed Hodge structure on moduli spaces of representations of the fundamental groupof a complex projective curve into a reductive algebraic group. Explicit formulas are obtained by counting points over ?nite ?elds on these moduli spaces |
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| Item Description: | Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| ISBN: | 9780817644178 |
| ISSN: | 2296-505X |
| Access: | Accès en ligne pour les établissements français bénéficiaires des licences nationales Accès soumis à abonnement pour tout autre établissement Conditions particulières de réutilisation pour les bénéficiaires des licences nationales. https://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 |