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Definability within structures related to Pascal’s triangle modulo an integer

Alexis Bès, Ivan Korec (1998)

Fundamenta Mathematicae

Let Sq denote the set of squares, and let S Q n be the squaring function restricted to powers of n; let ⊥ denote the coprimeness relation. Let B n ( x , y ) = ( x + y x ) M O D n . For every integer n ≥ 2 addition and multiplication are definable in the structures ⟨ℕ; Bn,⊥⟩ and ⟨ℕ; Bn,Sq⟩; thus their elementary theories are undecidable. On the other hand, for every prime p the elementary theory of ⟨ℕ; Bp,SQp⟩ is decidable.

Deformations and derived categories

Frauke M. Bleher, Ted Chinburg (2005)

Annales de l'institut Fourier

In this paper we generalize the deformation theory of representations of a profinite group developed by Schlessinger and Mazur to deformations of objects of the derived category of bounded complexes of pseudocompact modules for such a group. We show that such objects have versal deformations under certain natural conditions, and we find a sufficient condition for these versal deformations to be universal. Moreover, we consider applications to deforming Galois cohomology classes and the étale hypercohomology...

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