Webexploiting the classical theorem that the class-group is annihilated by the (Galois-module action of) the so-called Stickelberger ideal. Under some plausible number-theoretical hypothesis, our approach provides a close principal multiple in quantum polynomial time. Combined with thepreviousresults,thissolvesIdeal-SVPintheworstcaseinquantum WebAug 12, 2024 · Stickelberger's discriminant theorem for algebras. Stickelberger proved that the discriminant of a number field is congruent to 0 or 1 modulo 4. We generalize this to …
On the index of the Stickelberger ideal and the ... - ScienceDirect
In mathematics, Stickelberger's theorem is a result of algebraic number theory, which gives some information about the Galois module structure of class groups of cyclotomic fields. A special case was first proven by Ernst Kummer (1847) while the general result is due to Ludwig Stickelberger (1890). See more Let Km denote the mth cyclotomic field, i.e. the extension of the rational numbers obtained by adjoining the mth roots of unity to $${\displaystyle \mathbb {Q} }$$ (where m ≥ 2 is an integer). It is a Galois extension of See more • Gross–Koblitz formula • Herbrand–Ribet theorem • Thaine's theorem • Jacobi sum See more Stickelberger's Theorem Let F be an abelian number field. Then, the Stickelberger ideal of F annihilates the class group of F. Note that θ(F) itself need not be an annihilator, but any multiple of it in Explicitly, the … See more • PlanetMath page See more WebKummer [16] discovered that the Stickelberger ideal S∆ of the group ring Z[∆] annihilates the ideal class group of K. In [7, Theorem 136], Hilbert gave an alternative proof of this important theorem. A new ingredient of his proof is that it uses the theorem of Hilbert and Speiser on the ring of integers of a tame abelian extension over Q ... free intel drivers update
On a generalization of Stickelberger’s Theorem - ResearchGate
WebSTICKELBERGER AND THE EIGENVALUE THEOREM DAVID A. COX To David Eisenbud on the occasion of his 75th birthday. Abstract. This paper explores the relation between the … WebWe prove two versions of Stickelberger s Theorem for positive dimensions and use them to compute the connected and irreducible components of a complex algebraic variety. If the variety is given by polynomials of degree d in n variables, then our ... WebMar 1, 2015 · The theorem states that the Stickelberger element, θ = ∑ a = 1 p − 1 a σ a − 1 ∈ Z [ Gal ( F / Q)] is an annhilator for the class group of F, where p − 1 is the size of Gal ( F / Q). blue chip support