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"key conjectures" is correct and usable in written English.
It can be used to refer to theories or ideas that are important or critical to understanding a particular topic, and it typically implies that those ideas are not necessarily proven or accepted as fact. For example: "The key conjectures related to the Fukushima disaster are that a significant amount of radiation has been released and that there could be long-term health implications for people living nearby."
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This concept is tightly linked to two key conjectures on evolution of cells: existence of a complex, precellular, compartmentalized but extensively mixing and recombining pool of genes, and origin of the eukaryotic cell by archaeo-bacterial fusion.
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Despite early hiccups, number theorists say they have finally proved a key conjecture about prime numbers: that the smallest possible gap between two large prime numbers continues to shrink, relative to the natural logarithm of the smaller number, as the numbers increase.
As noted above, mathematical insights involve an intuitive yet not fully elaborated understanding of the key ideas behind a conjecture.
This suggests that producing any depictive gesture may help students glean some key ideas behind the conjecture; however, dynamic gestures may be associated with reasoning about relationships between geometric objects.
Observations show that both teachers and students use multimodal forms of talk using speech-accompanied gestures as a way to track the development of key ideas when exploring mathematical conjectures (Nathan, Walkington, Srisurichan, & Alibali, 2011).
Section 2.4 introduces the Edge of Chaos hypothesis, a CA-related conjecture playing a key role in complexity theory.
While much of the learning generated by this research will be on palliative care processes, there will also be key methodological messages about developing CMO conjectures early in a project and populating them with evidence.
Movements are designed to either be task-relevant, capturing some key relation of the subsequent geometry conjecture (Table 1), or task-irrelevant.
Certain conjectures about human memory are keys to the central idea.
The key assumptions of the IGT have been summarized in conjectures 1 8.
So we conjecture that the statistics method is the key factor causing differences in identification of selection sweeps.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com