A classical result of Hasse states that the norm principle holds for finite cyclic extensions of global fields, in other words local norms are global norms. We investigate the norm principle for finite dimensional commutative kale algebras over global fiel ...
Embeddings of maximal tori in classical groups over fields of characteristic not 2 are the subject matter of several recent papers. The aim of the present paper is to give necessary and sufficient conditions for such an embedding to exist, when the base fi ...
Many classical results concerning quadratic forms have been extended to Hermitian forms over algebras with involution. However, not much is known in the case of sesquilinear forms without any symmetry property. The present paper will establish a Witt cance ...
Let k be a field of characteristic ≠2, A be a central simple algebra with involution σ over k and W(A,σ) be the associated Witt group of hermitian forms. We prove that for all purely inseparable extensions L of k, the canonical map rL/k:W(A,σ)⟶W(AL,σL) is ...
Let k be a field, and let L be an etale k-algebra of finite rank. If a is an element of k(x), let X-a be the affine variety defined by N-L/k(x) = a. Assuming that L has at least one factor that is a cyclic field extension of k, we give a combinatorial desc ...
Cohomological Invariants for G-Galois Algebras and Self-Dual Normal Bases. We define degree two cohomological invariants for G-Galois algebras over fields of characteristic not 2, and use them to give necessary conditions for the existence of a self--dua ...
We give necessary and sufficient conditions for an orthogonal group defined over a global field of characteristic not equal 2 to contain a maximal torus of a given type. ...
The aim of this paper is to give new upper bounds for Euclidean minima of algebraic number fields. In particular, to show that Minkowski's conjecture holds for the maximal totally real subfields of cyclotomic fields of prime power conductor. ...
