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Record Nr. |
UNINA9910827648203321 |
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Autore |
Greenberg Ralph <1944-> |
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Titolo |
Iwasawa Theory, Projective Modules, and Modular Representations / / Ralph Greenberg |
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Pubbl/distr/stampa |
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Providence, Rhode Island : , : American Mathematical Society, , 2010 |
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©2010 |
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ISBN |
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Descrizione fisica |
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1 online resource (185 p.) |
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Collana |
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Memoirs of the American Mathematical Society, , 0065-9266 ; ; Number 922 |
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Disciplina |
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Soggetti |
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Iwasawa theory |
Curves, Elliptic |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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"May 2011, volume 211, number 992 (second of 5 numbers )." -- T.p. |
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Nota di bibliografia |
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Includes bibliographical references. |
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Nota di contenuto |
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""Contents""; ""Abstract""; ""Chapter 1. Introduction.""; ""1.1. Congruence relations.""; ""1.2. Selmer groups for elliptic curves.""; ""1.3. Behavior of Iwasawa invariants.""; ""1.4. Selmer atoms.""; ""1.5. Parity questions.""; ""1.6. Other situations.""; ""1.7. Organization and acknowledgements.""; ""Chapter 2. Projective and quasi-projective modules.""; ""2.1. Criteria for projectivity and quasi-projectivity.""; ""2.2. Nonzero -invariant.""; ""2.3. The structure of G/to.G .""; ""2.4. Projective dimension.""; ""Chapter 3. Projectivity or quasi-projectivity of XE0(K)."" |
""3.1. The proof of Theorem 1.""""3.2. Quasi-projectivity.""; ""3.3. Partial converses.""; ""3.4. More general situations.""; ""3.5. -extensions.""; ""Chapter 4. Selmer atoms.""; ""4.1. Various cohomology groups. Coranks. Criteria for vanishing.""; ""4.2. Selmer groups for E[p].""; ""4.3. Justification of (1.4.b) and (1.4.c).""; ""4.4. Justification of (1.4.d) and the proof of Theorem 2.""; ""4.5. Finiteness of Selmer atoms.""; ""Chapter 5. The structure of Hv(K, E).""; ""5.1. Determination of E,v().""; ""5.2. Determination of ""426830A E,v, ""526930B ."" |
""5.3. Projectivity and Herbrand quotients.""""Chapter 6. The case where is a p-group.""; ""Chapter 7. Other specific groups.""; ""7.1. The groups A4, S4, and S5.""; ""7.2. The group PGL2(Fp).""; ""7.3. The groups PGL2(Z/pr+1Z) for r 1.""; ""7.4. Extensions of (Z/pZ) by a p-group.""; |
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""Chapter 8. Some arithmetic illustrations.""; ""8.1. An illustration where 0 is empty.""; ""8.2. An illustration where 0 is non-empty.""; ""8.3. An illustration where the ""0365ss's have abelian image.""; ""8.4. False Tate extensions of Q.""; ""Chapter 9. Self-dual representations."" |
""9.1. Various classes of groups.""""9.2. groups.""; ""9.3. Some parity results concerning multiplicities.""; ""9.4. Self-dual representations and the decomposition map.""; ""Chapter 10. A duality theorem.""; ""10.1. The main result.""; ""10.2. Consequences concerning the parity of sE().""; ""Chapter 11. p-modular functions.""; ""11.1. Basic examples of p-modular functions.""; ""11.2. Some p-modular functions involving multiplicities.""; ""Chapter 12. Parity.""; ""12.1. The proof of Theorem 3.""; ""12.2. Consequences concerning WDel(E,) and WSelp(E,)."" |
""Chapter 13. More arithmetic illustrations.""""13.1. An illustration where E K/F is empty.""; ""13.2. An illustration where K Q(E[p]).""; ""13.3. An illustration where Gal(K/Q) is isomorphic to Bn or Hn.""; ""Bibliography"" |
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