In mathematics, a Frobenius splitting, introduced by Mehta and Ramanathan (1985), is a splitting of the injective morphism OX→F*OX from a structure sheaf OX of a characteristic p > 0 variety X to its image F*OX under the Frobenius endomorphism F*.
Brion & Kumar (2005) give a detailed discussion of Frobenius splittings.
A fundamental property of Frobenius-split projective schemes X is that the higher cohomology Hi(X,L) (i > 0) of ample line bundles L vanishes.
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under the Frobenius endomorphism F*. Brion & Kumar (2005) give a detailed discussion of Frobeniussplittings. A fundamental property of Frobenius-split projective...
The theory of the Frobenius element goes further, to identify an element of DPj/IPj for given j which corresponds to the Frobenius automorphism in the...
of Frobeniussplitting of algebraic varieties jointly with Vikram Bhagvandas Mehta in (Mehta & Ramanathan 1985). The notion of Frobeniussplitting led...
ISSN 0021-8693, MR 1338967 Mehta, V. B.; Ramanathan, A. (1985), "Frobeniussplitting and cohomology vanishing for Schubert varieties", Annals of Mathematics...
element of the subfield GF(p). It is called the Frobenius automorphism, after Ferdinand Georg Frobenius. Denoting by φk the composition of φ with itself...
Different ideal Dedekind domain Splitting of prime ideals in Galois extensions Decomposition group Inertia group Frobenius automorphism Chebotarev's density...
over 240 citations. van der Kallen, Wilberd (1993). Lectures on FrobeniusSplittings and B-modules. ISBN 978-81-85198-60-6; 98 pages{{cite book}}: CS1...
\|_{F}} is the Frobenius norm and T = P − 1 {\displaystyle T=P^{-1}} is from some suitably constrained set of sparse matrices. Under the Frobenius norm, this...
In linear algebra, the Frobenius companion matrix of the monic polynomial p ( x ) = c 0 + c 1 x + ⋯ + c n − 1 x n − 1 + x n {\displaystyle p(x)=c_{0}+c_{1}x+\cdots...
Nakayama, On the dimension of modules and algebras. II. Frobenius algebras and quasi-Frobenius rings, Nagoya Math. J. Volume 9 (1955), 1–16. Endo, Shizuo;...
general, such a structure is called a Frobenius algebra. As the name implies, these were introduced by Frobenius in the nineteenth century. They have been...
lemma Snake lemma Splitting lemma Matrix determinant lemma Matrix inversion lemma Burnside's lemma also known as the Cauchy–Frobenius lemma Frattini's...
domain, Dedekind domain, Prüfer domain Von Neumann regular ring Quasi-Frobenius ring Hereditary ring, Semihereditary ring Local ring, Semi-local ring...
each point are smooth distributions which are integrable in the sense of Frobenius. The integral manifolds of these distributions are totally geodesic submanifolds...
\operatorname {Gal} (E/F)} is cyclic of order n and generated by the Frobenius homomorphism. The field extension Q ( 2 , 3 ) / Q {\displaystyle \mathbb...
2) if P is irreducible, but most resolvents are not always separable. Frobenius endomorphism Pages 240-241 of Lang, Serge (1993), Algebra (Third ed.)...
{\displaystyle \alpha =g(T,U)} in E ∖ F {\displaystyle E\setminus F} , the Frobenius endomorphism shows that the element α p {\displaystyle \alpha ^{p}} lies...
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