On the Surjectivity of the Galois Representations Associated to Non-CM Elliptic Curves
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Bibliographic record
Abstract
Abstract Let E be an elliptic curve defined over ℚ, of conductor N and without complex multiplication. For any positive integer l , let ϕ l be the Galois representation associated to the l -division points of E . From a celebrated 1972 result of Serre we know that ϕ l is surjective for any sufficiently large prime l . In this paper we find conditional and unconditional upper bounds in terms of N for the primes l for which ϕ l is not surjective.
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Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.012 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.013 | 0.004 |
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