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A finite field is a field with a finite number of elements. For each prime power $q^k$, there is a unique (up to isomorphism) finite field with $q^k$ elements. Up to isomorphism, these are the only finite fields.

1 vote
0 answers
193 views

Classifications of cubic surfaces

Is there a known classification of singular cubic surfaces over finite fields?
1 vote
2 answers
318 views

Does there exist a surface over a finite field which contains three skew lines?

Does there exist an irreducible surface, other than Hermitian surface, in $\mathbb{P}^3 (\mathbb{F}_q)$ containing three skew lines? I know that this is true for Hermitian surface. In fact, at every …