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Peer-reviewedCC BYJournal of Number Theory

Explicit lower bounds on the conductors of elliptic curves and abelian varieties over number fields

  • Pierre Tchamitchian
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Abstract

Following the work of Mestre, we use Weil's explicit formulas to compute explicit lower bounds on the conductors of elliptic curves and abelian varieties over number fields, assuming that their associated L -functions are analytic L -functions. Moreover, we obtain lower bounds for the conductor of elliptic curves and abelian varieties over Q with specified bad reduction, under the same hypothesis. As an application, we prove, for certain number fields, the non-existence of abelian varieties with analytic L -function and with everywhere good reduction.

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Cite

BibTeXRIS
BibTeX
@article{tchamitchian2026explicit,
  title = {{Explicit lower bounds on the conductors of elliptic curves and abelian varieties over number fields}},
  author = {Pierre Tchamitchian},
  journal = {Journal of Number Theory},
  year = {2026},
  month = oct,
  doi = {10.1016/j.jnt.2026.06.014},
  url = {https://hal.science/hal-05838589v1},
  note = {CC BY},
}
RIS
TY  - JOUR
TI  - Explicit lower bounds on the conductors of elliptic curves and abelian varieties over number fields
AU  - Pierre Tchamitchian
PY  - 2026
DA  - 2026/10/26
JO  - Journal of Number Theory
DO  - 10.1016/j.jnt.2026.06.014
UR  - https://hal.science/hal-05838589v1
AB  - Following the work of Mestre, we use Weil's explicit formulas to compute explicit lower bounds on the conductors of elliptic curves and abelian varieties over number fields, assuming that their associated L -functions are analytic L -functions. Moreover, we obtain lower bounds for the conductor of elliptic curves and abelian varieties over Q with specified bad reduction, under the same hypothesis. As an application, we prove, for certain number fields, the non-existence of abelian varieties with analytic L -function and with everywhere good reduction.
SN  - 0022-314X
SN  - 1096-1658
ER  -