Basically, when 的 is used after a noun or pronoun it represents the genitive, possessive case: 我的 = my, 你的 = your, 他的 = his. The genitive case is always an adjective. 的 represents 's. That said, Chinese often omits 的:红色女装
"The primary sense [of 'of'] in Old English still was "away," but it
shifted in Middle English with use of the word to translate Latin de,
ex, and especially Old French de, which had come to be the substitute
for the genitive case. "Of shares with another word of the same
length, as, the evil glory of being accessory to more crimes against
grammar than any other." [Fowler]"
太阳是红色的。
(The) sun is red
早晨的太阳是红色的。
(The) early morning's sun is red
早晨的太阳为什么是红色的。
(The) early morning's sun why is red
(Because the atmosphere is an aerosol, it filters out blue. Early morning the sunlight travels through a lot more atmosphere, because it is coming from the side, so to speak.)
论点是错误的。
argument is flawed.
你的论点是错误的。
Your argument is flawed
你的论点的基础是错误的。
Your argument its base is flawed
你的论点的基础根本就是错误的。
Your argument its base fundamentally is flawed