Related papers: Equations for formally real meadows
In a recent paper, Freitas and Siksek proved an asypmtotic version of Fermat's Last Theorem for many totally real fields. We prove an extension of their result to generalized Fermat equations of the form $A x^p+B y^p+ C z^p=0$, where $A$,…
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We survey the 19th century development of the signature of a quadratic form, and the applications in the 20th and 21st century to the topology of manifolds and dynamical systems. Version 2 is an expanded and corrected version of Version 1,…
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One of the basic questions in number theory is to determine semi-simple l-adic representations of the absolute Galois group of a number field. In this paper, we discuss the question for two dimensional representations over a totally real…
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Meadows have been proposed as alternatives for fields with a purely equational axiomatization. At the basis of meadows lies the decision to make the multiplicative inverse operation total by imposing that the multiplicative inverse of zero…
The first-order formulation of the principal sigma model with a Lie group target space is performed. By using the dualisation of the algebra and the field content of the theory the field equations which are solely written in terms of the…