Generalizing and unifying the known theorems for difference and differential fields, it is
shown that for every finite free algebra scheme 𝒟 over a field A of characteristic zero, the …

Generalizing Atiyah extensions, we introduce and study differential abelian tensor
categories over differential rings. By a differential ring, we mean a commutative ring with an …

Jet and prolongation spaces Page 1 Journal of the Inst. of Math. Jussieu (2010) 9(2), 391–430
391 doi:10.1017/S1474748010000010 c Cambridge University Press 2010 JET AND …

We develop a Galois theory for linear differential equations equipped with the action of an
endomorphism. This theory is aimed at studying the difference algebraic relations among …

We develop a theory of tensor categories over a field endowed with abstract operators. Our
notion of a “field with operators”, derived from the work of Moosa and Scanlon, includes the …

We study algebraic and model-theoretic properties of existentially closed fields with an
action of a fixed finite group. Such fields turn out to be pseudo-algebraically closed in a …

We prove that the class of partial differential fields of characteristic zero with an
automorphism has a model companion. We then establish the basic model theoretic …

arXiv:1404.7475v3 [math.LO] 25 Nov 2015 Page 1 arXiv:1404.7475v3 [math.LO] 25 Nov 2015
EXISTENTIALLY CLOSED FIELDS WITH G-DERIVATIONS DANIEL HOFFMANN† AND …

We study integrating (that is expanding to a Hasse–Schmidt derivation) derivations, and
more generally truncated Hasse–Schmidt derivations, satisfying iterativity conditions given …

This thesis is primarily concerned with D-fields. These structures were introduced by Rahim
Moosa and Thomas Scanlon in their trilogy [51, 52, 53] in order to provide a common …