Stickelberger's theorem
WebNov 16, 2024 · In mathematics, Stickelberger's theorem is a result of algebraic number theory, which gives some information about the Galois module structure of class groups … WebA non-abelian Stickelberger theorem Note that, in particular, we are in case (i) if Gis isomorphic to the symmetric group on any number of elements, the quaternion group of …
Stickelberger's theorem
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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 … Web210 C[GK ] such that for all 03C8 E K. We call 03B8T,K the T-incomplete L-function evaluator at s = 0. The reader should note that the definition of 03B8T,K is " twisted" by the introduction of the complex conjugate character on the right in (1.2). DEFINITION 1.1: The element 03C9T,K = WK03B8T,K of C[GK ] is called the Stickelberger element of K/k relative to T.
WebSTICKELBERGER’S DISCRIMINANT THEOREM FOR ALGEBRAS ASHER AUEL, OWEN BIESEL, AND JOHN VOIGHT Abstract. Stickelberger proved that the discriminant of a number eld … WebTheorem 1.2 is not an exceptional one in the above conjectual sense (and the assumption on h− pn is satisfied for all n). In [7, Theorem 136], Hilbert gave his famous alternative proof of the Kummer-Stickelberger theorem for the class group of Q(ζ p) using the Hilbert-Speiser theorem. Fröhlich [3] generalized this argument for the
WebOct 1, 2007 · We give an explicit version of a classical theorem of Stickelberger on the representation of certain integers by binary quadratic forms. This is achieved by … 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 ...
WebOct 21, 2024 · A “Stickelberger’s Theorem” that focuses on ( 1.2) and ( 1.3) can be found in [ 2 ]. A common feature of these papers is that no reference to Stickelberger is given! An exception is [ 11 ], which refers to the wrong paper of Stickelberger.
Webadmissibility of it expresses essentially Stickelberger's theorem in Iwasawa theory (Note that Stickelberger's theorem is based on elementary calculations, and not difficult), and that the concrete content of a special case (i.e., Fermat variety case) of such a general difficult geometric theorem (i.e., the main theorem of the p- adic stylish crockery setsWebThe theorem follows by proving that ΔK ≡ 0 mod 2 implies ΔK ≡ 0 mod 4, and that ΔK ≡ 1 mod 2 implies ΔK ≡ 1 mod 4. Assume that 2 ΔK. Then there exists a prime p of K lying … stylish crocsWebMar 19, 2024 · The Stickelberger ideal $ S $ is an ideal in $ \mathbf Z [ G ] $ annihilating $ C $ and related with the relative class number $ h ^ {-} $ of $ K _ {m} $. It is defined as … pail for waterWebAug 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 … pail fingernailsWebAug 12, 2024 · W e prove this theorem using purely linear algebra techniques (as Theorem 3.1), giving a new proof of Stickelberger’s theorem even in the case of the ring of integers of a num ber field. pail for constructionWebFeb 9, 2024 · Stickelberger’s theorem Theorem 1 (Stickelberger). Let L= Q(ζm) L = Q ( ζ m) be a cyclotomic field extension of Q Q with Galois group G= {σa}a∈(Z/mZ)× G = { σ a } a ∈ ( Z / m Z) ×, and consider the group ring Q[G] Q [ G]. Define the Stickelberger element θ∈ Q[G] θ ∈ Q [ G] by and take β∈ Z[G] β ∈ Z [ G] such that βθ∈Z[G] β θ ∈ Z [ G] as well. pail flush bowlWebI was going through the proof of Stickelberger's theorem about discriminants in the book 'Algebraic Number Theory' by Richard A. Mollin, and I am having some problems in … pail full of water