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searching for Frobenius endomorphism 8 found (93 total)

Supersingular prime (algebraic number theory) (350 words) [view diff] exact match in snippet view article

using heuristics involving the distribution of eigenvalues of the Frobenius endomorphism. As of 2019, this conjecture is open. More generally, if K is any

Ree group (2,067 words) [view diff] exact match in snippet view article find links to article

the automorphism is the Frobenius endomorphism of F, while for the Steinberg groups the automorphism is the Frobenius endomorphism times an automorphism

Enriques surface (1,050 words) [view diff] exact match in snippet view article find links to article

Singular: dim(H1(O)) = 1 and is acted on non-trivially by the Frobenius endomorphism. This implies K = 0, and Picτ is μ2. The surface is a quotient of

Drinfeld module (1,623 words) [view diff] exact match in snippet view article find links to article

acting as multiplication and τ {\displaystyle \tau } acting as the Frobenius endomorphism of L {\displaystyle L} . The ring L { τ } {\displaystyle L\{\tau

Supersingular elliptic curve (2,351 words) [view diff] exact match in snippet view article find links to article

over K is supersingular if and only if the trace of the q-power Frobenius endomorphism is congruent to zero modulo p. When q=p is a prime greater than

Counting points on elliptic curves (2,454 words) [view diff] exact match in snippet view article find links to article

is called an Elkies prime if the characteristic equation of the Frobenius endomorphism, ϕ 2 − t ϕ + q = 0 {\displaystyle \phi ^{2}-t\phi +q=0} , splits

Fermat's theorem on sums of two squares (6,609 words) [view diff] exact match in snippet view article find links to article

is even. Hence the right hand side equals ω, so in this case the Frobenius endomorphism of Z[i]/(p) is the identity. Kummer had already established that

Witt vector (7,686 words) [view diff] exact match in snippet view article find links to article

characteristic p ring to characteristic 0 together with a lift of its Frobenius endomorphism. To make this precise, define a δ {\displaystyle \delta } -ring