MSC2020 · 11Gxx

Arithmetic algebraic geometry (Diophantine geometry)

Arithmetic algebraic geometry (Diophantine geometry) [See also 11Dxx, 14Gxx, 14Kxx]

6 mapped entries · Browse and filter all →

Counts include all statuses and descendants. Classifications are editorial or inferred from community fields, not an AMS assessment of the problem.

Subcategories

11G05Elliptic curves over global fields1 11G07Elliptic curves over local fields0 11G09Drinfel'd modules; higher-dimensional motives, etc.0 11G10Abelian varieties of dimension

> 1

0 11G15Complex multiplication and moduli of abelian varieties0 11G16Elliptic and modular units0 11G18Arithmetic aspects of modular and Shimura varieties0 11G20Curves over finite and local fields2 11G25Varieties over finite and local fields0 11G30Curves of arbitrary genus or genus

\ne 1

over global fields2 11G32Arithmetic aspects of dessins d'enfants, Bely? theory0 11G35Varieties over global fields0 11G40

L

-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture0 11G42Arithmetic mirror symmetry0 11G45Geometric class field theory0 11G50Heights1 11G55Polylogarithms and relations with

K

-theory0 11G99Arithmetic algebraic geometry (Diophantine geometry)0

Mapped problems

OP-12097Number theoryOpen

Essential minimum of the Zhang-Zagier height ( $C_{82}$ )

Essential minimum of the Zhang-Zagier height: determine C 82 or improve its bounds; the repository records 0.24874 (lower) and 0.2536331090204145 (upper).

Optimization Constants in Mathematics — Davis, Ivanisvili & Tao· Licensed source statement· 2026

OP-12043Number theoryOpen

Ihara constant over $\mathbb{F}_2$ ( $C_{33}$ )

Ihara constant over mathbb F 2 : determine C 33 or improve its bounds; the repository records 0.316999... (lower) and sqrt 2 -1 approx 0.41421 (upper).

Optimization Constants in Mathematics — Davis, Ivanisvili & Tao· Licensed source statement· 2026

OP-11959Number theorySolved

Many Rational Points on a Genus-2 Curve

Many Rational Points on a Genus-2 Curve. Moderately interesting problem from Epoch AI’s FrontierMath: Open Problems; answers are checked by a verifier program.

Epoch AI — FrontierMath: Open Problems· Licensed source statement· 2026

OP-11958Number theorySolved

A Genus 2 Curve over the Rationals with a Rational Torsion Point of Prime Order at Least 31

A Genus 2 Curve over the Rationals with a Rational Torsion Point of Prime Order at Least 31. Moderately interesting problem from Epoch AI’s FrontierMath: Open Problems; answers are checked by a verifier program.

Epoch AI — FrontierMath: Open Problems· Licensed source statement· 2026

OP-11956Number theorySolved

Elliptic Curves over $\mathbb{Q}$ of Large Rank

Elliptic Curves over mathbb Q of Large Rank. Moderately interesting problem from Epoch AI’s FrontierMath: Open Problems; answers are checked by a verifier program.

Epoch AI — FrontierMath: Open Problems· Licensed source statement· 2026

OP-11955Number theoryOpen

Elliptic Curves with Prescribed Number of Points

Elliptic Curves with Prescribed Number of Points. Solid result problem from Epoch AI’s FrontierMath: Open Problems; answers are checked by a verifier program.

Epoch AI — FrontierMath: Open Problems· Licensed source statement· 2026