{"text_format":"2","workbook":"xls","n_sheets":1,"sheets":["report2"],"not_rendered":{"charts":0,"images":0,"macros":0,"external_links":1,"defined_names":1,"comments":0,"pivot_tables":0},"unopened":[],"bounds":{"document_bytes":16777216,"sheet_cells":100000,"run_cost":"one","rows_first":2000,"rows_last":500,"rows_between":2000,"halvings":0,"cell_chars":16384,"cell_head_chars":4096},"cells_cut":0,"cells_raw":0,"read":"whole","date_system":"1900","formulas":"cached_only"}

{"sheet":"report2","index":0,"n_rows":22,"n_cols":5,"rows_kept":22,"cut":false,"hidden":false,"merged":[[0,2,0,3],[0,4,0,5],[1,2,1,3],[1,4,1,5],[2,2,2,3],[2,4,2,5],[3,2,3,3],[5,2,5,3],[6,2,6,3],[7,2,7,3],[8,2,8,3],[9,2,9,3],[11,2,11,3],[12,2,12,3],[16,2,16,3]],"flags":["formulas_cached_only"]}
[null,"1.","Record Nr.",null,"UNINA9910827648203321"]
[null,null,"Autore",null,"Greenberg Ralph <1944->"]
[null,null,"Titolo",null,"Iwasawa Theory, Projective Modules, and Modular Representations / / Ralph Greenberg"]
[null,null,"Pubbl/distr/stampa",null,"Providence, Rhode Island : , : American Mathematical Society, , 2010"]
[{"$nulls":4},"©2010"]
[null,null,"ISBN",null,"1-4704-0609-8"]
[null,null,"Descrizione fisica",null,"1 online resource (185 p.)"]
[null,null,"Collana",null,"Memoirs of the American Mathematical Society, , 0065-9266 ; ; Number 922"]
[null,null,"Disciplina",null,"512.7/4"]
[null,null,"Soggetti",null,"Iwasawa theory"]
[{"$nulls":4},"Curves, Elliptic"]
[null,null,"Lingua di pubblicazione",null,"Inglese"]
[null,null,"Formato",null,"Materiale a stampa"]
[null,null,null,"Livello bibliografico","Monografia"]
[null,null,null,"Note generali","\"May 2011, volume 211, number 992 (second of 5 numbers ).\" -- T.p."]
[null,null,null,"Nota di bibliografia","Includes bibliographical references."]
[null,null,"Nota di contenuto",null,"\"\"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).\"\""]
[{"$nulls":4},"\"\"3.1. The proof of Theorem 1.\"\"\"\"3.2. Quasi-projectivity.\"\"; \"\"3.3. Partial converses.\"\"; \"\"3.4. More general situations.\"\"; \"\"3.5. -extensions.\"\"; \"\"Chapter 4. Selmer atoms.\"\"; \"\"4.1. Various cohomology groups. Coranks. Criteria for vanishing.\"\"; \"\"4.2. Selmer groups for E[p].\"\"; \"\"4.3. Justification of (1.4.b) and (1.4.c).\"\"; \"\"4.4. Justification of (1.4.d) and the proof of Theorem 2.\"\"; \"\"4.5. Finiteness of Selmer atoms.\"\"; \"\"Chapter 5. The structure of Hv(K, E).\"\"; \"\"5.1. Determination of E,v().\"\"; \"\"5.2. Determination of \"\"426830A E,v, \"\"526930B .\"\""]
[{"$nulls":4},"\"\"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.\"\"; \"\"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 "]
[{"$nulls":4},"extensions of Q.\"\"; \"\"Chapter 9. Self-dual representations.\"\""]
[{"$nulls":4},"\"\"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,).\"\""]
[{"$nulls":4},"\"\"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\"\""]