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An Eisenstein ideal for imaginary quadratic fields and the Bloch-Kato conjecture for Hecke characters
| Content Provider | Semantic Scholar |
|---|---|
| Author | Berger, Tobias |
| Copyright Year | 2005 |
| Abstract | For certain algebraic Hecke characters χ of an imaginary quadratic field F we define an Eisenstein ideal in a p-adic Hecke algebra acting on cuspidal automorphic forms of GL2/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 special L-value L(0, χ). We further prove that its index is bounded from above by the order of the Selmer group of the p-adic Galois character associated to χ−1. This uses the work of R. Taylor et al. on attaching Galois representations to cuspforms of GL2/F . Together these results imply a lower bound for the size of the Selmer group in terms of L(0, χ), coinciding with the value given by the Bloch-Kato conjecture. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://arxiv.org/pdf/math/0701177v1.pdf |
| Language | English |
| Access Restriction | Open |
| Subject Keyword | Bloch sphere Class Eisenstein series Imaginary time Linear algebra Personality Character |
| Content Type | Text |
| Resource Type | Article |
