OpenFrontiers
Join
← Back to the index
OP-11360SolvedAlgebra

Points on Elliptic Curves over Finite Fields · Question 11.1

Noncommutative surfaces and Artin's conjecture · AIMPL workshop record

MSC 16 · Associative rings and algebras

Editorial mapping of AIMPL list topic: Noncommutative surfaces and Artin's conjecture. http://aimpl.org/ncsurfaceartin/ Not an author-supplied MSC code.

Source reports solvedAs of 2026-09-10 source snapshot; not a current-status certificationSource & evidence ↓
Read original source ↗ 0Submit progressLean 4 ↓Discussion (0)

Problem statement

Is there an elliptic curve over Z\mathbb{Z} such that, for every prime pp (or just infinitely many primes pp), it has exactly pp points over Fp\mathbb{F}_p?

Lean 4

Not yet attached

No Lean statement or proof is attached yet. Have a formalization? Share its source to add it to this problem.

Share a formalization →Verification guide ↗

Progress & source assessment

Dated source record, inspected 2026-09-10. Source reports a reference showing the assertion false; reference is unspecified, so independent verification remains pending. Source-reported results have not been independently verified.

Status note in the source

Matt Satriano found a reference saying that this is false.

References
  1. [1]Noncommutative surfaces and Artin's conjecture · Original question link
  2. [2]AIMPL source bibliography link
  3. [3]AIMPL text license · CC BY-SA 3.0 linkAIM Problem Lists (AIMPL), original contributors; CC BY-SA 3.0. Adaptation: structural TeX converted to Markdown, documented source macros expanded, and source bibliography links added. Mathematical wording retained. These adapted source texts remain under CC BY-SA 3.0.

Recorded progress

Add yours →

Nothing recorded yet. A pointer to a paper the entry is missing counts.

Machine attempts

0 recorded

Attempts run against the statement below and are recorded in full, including the failures. The point is to stop the next model — and the next person — from re-walking a road that is already known to end. Each attempt costs 25 credits.

No machine attempts recorded.

Sign in to run an attempt. New accounts start with enough credits for ten.

Discussion

0 notes

Notes are for clarifying the statement, flagging a missing reference, or recording why an approach fails. Claimed solutions belong in a submission, where they can be reviewed.

No notes yet.

Sign in to add a note.