In a sense, it is just a convention. The fundamental theorem of Galois theory gives an inclusion-reversing bijection between the subgroups of the Galois group and the intermediate fields of the splitting field. If I had drew the diagram respecting this bijection, then the splitting field would be on the bottom and the base field Q would be on top. However, we (mathematicians) prefer "larger" objects to be higher in our pictures and so we flip the diagram so that the splitting field ends up on top.
@@AdamGlesser ah I see thank you. I think I am more familiar with the reverse convention, but as they say mathematics is what presists over changes of notation.
I am not sure I see why Q is on the bottom and the splitting field is on the top.
In a sense, it is just a convention. The fundamental theorem of Galois theory gives an inclusion-reversing bijection between the subgroups of the Galois group and the intermediate fields of the splitting field. If I had drew the diagram respecting this bijection, then the splitting field would be on the bottom and the base field Q would be on top. However, we (mathematicians) prefer "larger" objects to be higher in our pictures and so we flip the diagram so that the splitting field ends up on top.
@@AdamGlesser ah I see thank you. I think I am more familiar with the reverse convention, but as they say mathematics is what presists over changes of notation.