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On the section conjecture over function fields and finitely generated fields
| Content Provider | Semantic Scholar |
|---|---|
| Author | Saidi, Mohamed |
| Copyright Year | 2015 |
| Abstract | We investigate sections of arithmetic fundamental groups of hyperbolic curves over function fields. As a consequence we prove that the anabelian section conjecture of Grothendieck holds over all finitely generated fields over $\Bbb Q$ if it holds over all number fields, under the condition of finiteness (of the $\ell$-primary parts) of certain Shafarevich-Tate groups. We also prove that if the section conjecture holds over all number fields then it holds over all finitely generated fields for curves which are defined over a number field. |
| Starting Page | 335 |
| Ending Page | 357 |
| Page Count | 23 |
| File Format | PDF HTM / HTML |
| DOI | 10.4171/PRIMS/184 |
| Alternate Webpage(s) | https://ore.exeter.ac.uk/repository/bitstream/handle/10871/21929/ON%20THE%20SECTION%20CONJECTURE%20OVER%20FUNCTION.pdf?isAllowed=y&sequence=1 |
| Alternate Webpage(s) | https://arxiv.org/pdf/1512.01207v3.pdf |
| Alternate Webpage(s) | https://doi.org/10.4171/PRIMS%2F184 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
