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under (influence, control, conditions, etc. of); during (war, occupation, etc.)
「下」 has other readings with different meanings.
彼の指導の下で学んだ。
I studied under his guidance.
厳しい条件の下で仕事をしている。
I work under strict conditions.
この制度の下では自由に意見を言うのが難しいだろう。
Under this system, it would be difficult to speak freely.