| Data: |
2002 |
| Resum: |
For an algebraic number field k and a prime number p (if p = 2, we assume that µ4 [contained in] k), we study the maximal rank [rho]k of a free pro-p-extension of k. We give various interpretations of 1+r2(k)-[rho]k. The first uses Iwasawa theory, the second uses the envelope of a module and the third is local-global. These expressions confirm that 1 + r2 - [rho]k is related to the torsion of a certain Iwasawa module, hence to the dualizing module of a certain Galois group (under Leopoldt's conjecture). |
| Drets: |
Tots els drets reservats.  |
| Llengua: |
Francès |
| Document: |
Article ; recerca ; Versió publicada |
| Publicat a: |
Publicacions matemàtiques, V. 46 N. 1 (2002) , p. 201-219, ISSN 2014-4350 |
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