Download PDFOpen PDF in browserA general framework for geometric dualities for varieties of algebras4 pages•Published: July 28, 2014AbstractWe set up a framework that subsumes many important dualities in mathematics (Birkhoff, Stone, Priestly, Baker-Beynon, etc.) as well as the classical correspondence between polynomial ideals and affine varieties in algebraic geometry. Our main theorems provide a generalisation of Hilbert's Nullstellensatz to any (possibly infinitary) variety of algebras. The common core of the above dualities becomes then clearly visible and sets the basis to a canonical method to seek for a geometric dual to any given variety of algebras.Keyphrases: algebraic geometry, categorical adjunction, galois adjunction, hilbert nullstellensatz, stone dualities, topological duality, universal algebra In: Nikolaos Galatos, Alexander Kurz and Constantine Tsinakis (editors). TACL 2013. Sixth International Conference on Topology, Algebra and Categories in Logic, vol 25, pages 213-216.
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