のもとで

1. 1Under the guidance, supervision, or influence of a person or authority.Ex. 1
2. 2Under certain conditions, arrangements, or with someone's cooperation or support.Ex. 2

Common in written and formal contexts such as reports, news, and descriptions of research or training. It frames the action as happening within someone's sphere of influence, guidance, or support, or under a set of conditions. Typical nouns include 指導, 監督, 協力, 条件, and names or titles of people such as a teacher or mentor.

• 1.
  にあってN1「にあって」 also attaches to nouns and has a formal, written tone, but it emphasizes the special period, environment, or status one is in, and can introduce either a logical consequence or a contrast. 「のもとで」 instead highlights being influenced and constrained by someone's actions or by conditions and systems, so the two are generally not interchangeable.
• 2.
  において / におけるN3「において」 only indicates the place, occasion, time, or field involved and carries no sense of being governed or protected, while 「のもとで」 emphasizes being influenced and constrained by someone's actions or by conditions and institutions. 「において」 attaches directly to a noun, and the two are generally not interchangeable.
• 3.
  に基づいてN2「に基づいて」 centers on acting with data or rules as the basis, while 「のもとで」 centers on being within the scope of someone's influence or of conditions and systems. With 「法・指導」 both are possible: the former means acting according to their content, the latter means proceeding under their constraints or guidance.
• 4.
  を通じて / を通してN2「を通じて／を通して」 uses a person or thing as a medium, or expresses running through an entire period or scope, while 「のもとで」 means being under someone's guidance, protection, or certain conditions. The former is stylistically neutral while the latter is more formal and written, so they generally cannot be interchanged.
• 5.
  上でN3「上で」 attaches to the た形 or dictionary form of verbs, or to 「名詞の」, and means 'after doing..., then...' or 'in the area of...'; 「のもとで」 attaches only to 「名詞の」 and means being within the framework of someone's influence or conditions. With nouns like 「同意」, the two can often be interchanged.
• 6.
  の中でN4「の中で」 is used for comparing within a range or group (often paired with 「一番」) or for being inside a space or situation, and carries no sense of being guided, governed, or bound by a framework. It is stylistically neutral and can also attach to the た形 of verbs, so the two are generally not interchangeable.

Unlike において, which marks the place or field where something occurs, にあって, which stresses being in a situation, and の中で, which means within a group or space, のもとで stresses being under someone's influence, guidance, or conditions. It also differs from に基づいて (acting on a basis or standard), を通じて (acting through a means or intermediary), and 上で (in the process or respect of doing something).