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On the Eisenstein ideal for imaginary quadratic fields
| Content Provider | Scilit |
|---|---|
| Author | Berger, Tobias |
| Copyright Year | 2009 |
| Description | Journal: Compositio Mathematica For certain algebraic Hecke charactersχof an imaginary quadratic fieldFwe define an Eisenstein ideal in ap-adic Hecke algebra acting on cuspidal automorphic forms of $GL_{2/F}$. By finding congruences between Eisenstein cohomology classes (in the sense of G. Harder) and cuspidal classes we prove a lower bound for the index of the Eisenstein ideal in the Hecke algebra in terms of the specialL-valueL(0,χ). We further prove that its index is bounded from above by thep-valuation of the order of the Selmer group of thep-adic Galois character associated $toχ^{−1}$. This uses the work of R. Tayloret al. on attaching Galois representations to cuspforms of $GL_{2/F}$. Together these results imply a lower bound for the size of the Selmer group in terms ofL(0,χ), coinciding with the value given by the Bloch–Kato conjecture. |
| Ending Page | 632 |
| Starting Page | 603 |
| ISSN | 00221295 |
| e-ISSN | 15705846 |
| DOI | 10.1112/s0010437x09003984 |
| Journal | Compositio Mathematica |
| Issue Number | 3 |
| Volume Number | 145 |
| Language | English |
| Publisher | Wiley-Blackwell |
| Publisher Date | 2009-04-15 |
| Access Restriction | Open |
| Subject Keyword | Journal: Compositio Mathematica Bloch-kato Conjecture Selmer Groups Congruences of Modular Forms Eisenstein Cohomology Galois Representation Modular Form Automorphic Form Number Theory Lower Bound |
| Content Type | Text |
| Resource Type | Article |
| Subject | Algebra and Number Theory |
