We analyze the notions of indiscernibility and indeterminacy in the light of the Galois theory of field extensions and the generalization to K -algebras proposed by Grothendieck. Grothendieck’s reformulation of Galois theory permits to recast the Galois correspondence between symmetry groups and invariants as a Galois– Grothendieck duality between G-spaces and the minimal observable algebras th...

Galois geometries and coding theory are two research areas which have been interacting with each other for many decades. From the early examples linking linear MDS codes with arcs in finite projective spaces, linear codes meeting the Griesmer bound with minihypers, covering radius with saturating sets, links have evolved to functional codes, generalized projective Reed–Muller codes, and even fu...

This paper presents works on reducible polynomials in Galois theory. It gives a fundamental theorem about the Galois ideals associated with a product of groups. These results are used for the practical determination of Galois groups of polynomials of degrees up to 7. : : :). The following tools are used: resolvents (relative or absolute), p-adic methods, Grr obner bases or block systems. In gen...

To a large extent, the investigations to be brought up today arise from a curious inadequacy having to do with the arrow on the left. On the one hand, it is widely acknowledged that the theory of motives finds a strong source of inspiration in Diophantine geometry, inasmuch so many of the structures, conjectures, and results therein have as model the conjecture of Birch and Swinnerton-Dyer, whe...

The category of finite dimensional modules for the proalgebraic differential Galois group of the differential Galois theoretic closure of a differential field F is equivalent to the category of finite dimensional F spaces with an endomorphism extending the derivation of F . This paper presents an expository proof of this fact modeled on a similar equivalence from polynomial Galois theory, whose...

Let a < vδ,W be arbitrary. I. Clairaut’s extension of subsets was a milestone in parabolic group theory. We show that ∆′ < ∞. Recently, there has been much interest in the derivation of parabolic, linear, non-Abel–Riemann ideals. In [24, 26, 28], the authors examined graphs.

The study of rhythmic canons by mathematicians with musical interest has given rise to unexpected connections to non trivial mathematical problems. The author tried a new approach based on a Galoisian interpretation of the novel results and concepts of Coven and Meyerowitz [4]. Extending this in a second part to finite fields, he concludes with unexpected results. 1 Rhythmic canons, tiling the ...

A generalization of Serre’s Conjecture asserts that if F is a totally real field, then certain characteristic p representations of Galois groups over F arise from Hilbert modular forms. Moreover, it predicts the set of weights of such forms in terms of the local behaviour of the Galois representation at primes over p. This characterization of the weights, which is formulated using p-adic Hodge ...

On modular Galois representations modulo prime powers Chen, Imin; Kiming, Ian; Wiese, Gabor Published in: International Journal of Number Theory DOI: 10.1142/S1793042112501254 Publication date: 2013 Document Version Publisher's PDF, also known as Version of record Citation for published version (APA): Chen, I., Kiming, I., & Wiese, G. (2013). On modular Galois representations modulo prime power...

We examine basic notions of categorical Galois theory for the adjunction between Π0 and the inclusion as discrete, in the case of simplicial complexes. Covering morphisms are characterized as the morphisms satisfying the unique simplex lifting property, and are classified by means of the fundamental groupoid, for which we give an explicit “Galoistheoretic” description. The class of covering mor...