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Results tagged with finite-fields
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user 4008
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.
25
votes
Accepted
How does Tate verify his own conjecture for the Fermat hypersurface?
I don't know how Tate did it but here is one way. Let $\zeta$ be such that
$\zeta^{q+1}=-1$ and put $a_j=(0\colon\cdots\colon1\colon\zeta:\cdots\colon0)$,
$j=0,\ldots,i$ with the $1$ in coordinate $2 …
- 22.6k
1
vote
A family of hypersurfaces with many points
This is very far from a solution but just some ideas that could be possibly be
used as a start.
First a simple observation on an Artin-Schreier type extension $X\rightarrow Y$,
where $X:=\mathrm{Spec …
- 22.6k