On order of vanishing of characteristic elements
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Meng Fai Lim
Abstract
Let p be a fixed odd prime. Let E be an elliptic curve defined over a number field F with either good ordinary reduction or multiplicative reduction at each prime of F above p. We shall study the characteristic element of the Selmer group of E over a p-adic Lie extension. In particular, we relate the order of vanishing of these characteristic elements evaluated at Artin representations to the Selmer coranks and their twists in the intermediate subextensions of the p-adic Lie extension.
Funding source: National Natural Science Foundation of China
Award Identifier / Grant number: 11771164
Funding source: Fundamental Research Funds for the Central Universities
Award Identifier / Grant number: CCNU20TD002
Funding statement: This research is supported by the National Natural Science Foundation of China under Grant No. 11771164, and the Fundamental Research Funds for the Central Universities of CCNU under Grant No. CCNU20TD002.
Acknowledgements
We thank the anonymous referee for the many helpful comments and suggestions.
References
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© 2022 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Approximating the group algebra of the lamplighter by infinite matrix products
- Shift invariance and reflexivity of compressions of multiplication operators
- Non-invariant deformations of left-invariant complex structures on compact Lie groups
- On the gaps between consecutive primes
- Trivial cup products in bounded cohomology of the free group via aligned chains
- Iwasawa invariants for elliptic curves over ℤp-extensions and Kida's formula
- Estimates of covering type and minimal triangulations based on category weight
- Coherent categorical structures for Lie bialgebras, Manin triples, classical r-matrices and pre-Lie algebras
- Stable vector bundles on generalized Kummer varieties
- Dirac series for complex 𝐸7
- On order of vanishing of characteristic elements
- On transitivity-like properties for torsion-free Abelian groups
- Reverse convolution inequalities for Lebedev–Skalskaya transforms
- Existence of weak solutions to a general class of diffusive shallow medium type equations
Articles in the same Issue
- Frontmatter
- Approximating the group algebra of the lamplighter by infinite matrix products
- Shift invariance and reflexivity of compressions of multiplication operators
- Non-invariant deformations of left-invariant complex structures on compact Lie groups
- On the gaps between consecutive primes
- Trivial cup products in bounded cohomology of the free group via aligned chains
- Iwasawa invariants for elliptic curves over ℤp-extensions and Kida's formula
- Estimates of covering type and minimal triangulations based on category weight
- Coherent categorical structures for Lie bialgebras, Manin triples, classical r-matrices and pre-Lie algebras
- Stable vector bundles on generalized Kummer varieties
- Dirac series for complex 𝐸7
- On order of vanishing of characteristic elements
- On transitivity-like properties for torsion-free Abelian groups
- Reverse convolution inequalities for Lebedev–Skalskaya transforms
- Existence of weak solutions to a general class of diffusive shallow medium type equations
