Last Updated
：2025/12/04
diophantine geometry
Noun
(mathematics)
A
developing
branch
of
mathematics
in
which
techniques
of
algebraic
geometry
are
applied
to
number
theory
(specifically
the
theory
of
Diophantine
equations),
in
particular
being
concerned
with
algebraic
varieties
over
fields
that
are
finitely
generated
over
their
prime
fields
and
over
local
fields.
Japanese Meaning
ディオファントス幾何学：代数幾何学の技法をディオファントス方程式や、素体上または局所体上で有限生成された体上の代数多様体に適用し、数論（特に整数解の問題）を研究する発展途上の数学分野
Sense（1）
(mathematics)
A
developing
branch
of
mathematics
in
which
techniques
of
algebraic
geometry
are
applied
to
number
theory
(specifically
the
theory
of
Diophantine
equations),
in
particular
being
concerned
with
algebraic
varieties
over
fields
that
are
finitely
generated
over
their
prime
fields
and
over
local
fields.
Quizzes for review
(mathematics) A developing branch of mathematics in which techniques of algebraic geometry are applied to number theory (specifically the theory of Diophantine equations), in particular being concerned with algebraic varieties over fields that are finitely generated over their prime fields and over local fields.
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diophantine geometry
Recent breakthroughs in diophantine geometry have deepened our understanding of rational points on algebraic varieties.
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Recent breakthroughs in diophantine geometry have deepened our understanding of rational points on algebraic varieties.
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