Book section
Remark on fundamental groups and effective Diophantine methods for hyperbolic curves
- Abstract:
- In a letter from Grothendieck to Faltings, it was suggested that a positive answer to the section conjecture should imply finiteness of points on hyperbolic curves over number fields. In this paper, we point out instead the analogy between the section conjecture and the finiteness conjecture for the Tate-Shafarevich group of elliptic curves. That is, the section conjecture should provide a terminating algorithm for finding all rational points on a hyperbolic curve equipped with a rational point.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
Actions
Access Document
- Files:
-
-
(Preview, Author's original, pdf, 130.3KB, Terms of use)
-
- Publisher copy:
- 10.1007/978-1-4614-1260-1_16
Authors
Contributors
+ Goldfeld, D
- Role:
- Editor
+ Jorgenson, J
- Role:
- Editor
+ Jones, P
- Role:
- Editor
+ Ramakrishnan, D
- Role:
- Editor
+ Ribet, K
- Role:
- Editor
- Publisher:
- Springer US
- Journal:
- Number Theory, Analysis and Geometry : In Memory of Serge Lang More from this journal
- Pages:
- 355-368
- Publication date:
- 2011-11-04
- DOI:
- EISBN:
- 978-1-4614-1260-1
- ISBN:
- 978-1-4614-1259-5
- Language:
-
English
- Keywords:
- Pubs id:
-
pubs:308583
- UUID:
-
uuid:a264fd12-819b-4dc0-b7c7-e9cc364d2b1e
- Local pid:
-
pubs:308583
- Source identifiers:
-
308583
- Deposit date:
-
2012-12-19
- ARK identifier:
Terms of use
- Copyright holder:
- Springer Science+Business Media, LLC
- Copyright date:
- 2012
- Rights statement:
- © Springer Science+Business Media, LLC 2012
- Notes:
- This is the accepted manuscript version of the chapter. The final version is available online from Springer at https://doi.org/10.1007/978-1-4614-1260-1_16
If you are the owner of this record, you can report an update to it here: Report update to this record