Word for "a deep study"

What first came to mind was:

delve: to carry on intensive and thorough research for data, information, or the like; investigate: to delve into the issue of prison reform.

Usually used with into, as in the example above.

Source: dictionary.com

As stated in the comments, investigation is the word that you are looking for.

A formal inquiry or systematic study

(OED)

This was called a deep dive where I used to work:

an in-depth exploration

It's mostly used in the noun sense in business. "Tsk. We'll have to perform a deep-dive on this" or "let's do a deep dive on this tomorrow." It can mean exhaustively examining every facet of an issue.

It's a good noun to use in conjunction with the verb delve suggested earlier. A noun is needed in the business sense because a "deep dive" begins to take on a certain scheduled ominousness in the noun sense like exam, test, audit and review.