We give upper bounds for the differential Nullstellensatz in the case of ordinary systems of differential algebraic equations over any field of constants K of characteristic 0. Let x be a set of n differential variables, ...

Given a finite-dimensional monomial algebra A, we consider the trivial extension TA and provide formulae, depending on the characteristic of the field, for the dimensions of the summands HH1(A) and Alt(DA) of the first ...

The worldline formalism is a useful scheme in quantum field theory which has also become a powerful tool for numerical computations. The key ingredient in this formalism is the first quantization of an auxiliary point-particle ...

We consider associative algebras λ over a field provided with a direct sum decomposition of a two-sided ideal M and a sub-algebra A - examples are provided by trivial extensions or triangular type matrix algebras. In this ...

Recent advances in computational techniques for K-theory allow us to describe the K-theory of toric varieties in terms of the K-theory of fields and simple cohomological data.

We prove without any assumption on the ground field that higher Hochschild homology groups do not vanish for two large classes of algebras whose global dimension is not finite.

LetRn be the ring of Laurent polynomials in n variables over a field k of characteristic zero and letKn be its fraction field. Given a linear algebraic κ-groupG,we showthat aKn-torsor under G which is unramified with respect ...

Given a finite dimensional algebra over a perfect field the text introduces covering functors over the mesh category of any modulated Auslander–Reiten component of the algebra. This is applied to study the composition of ...

Let F be a differential field of characteristic 0, t=t1,…,tm a finite set of differential indeterminates over F and G⊂F〈t〉 a differential field extension of F, generated by nonconstant rational functions α1,…,αn of total ...

We count points over a finite field on wild character varieties of Riemann surfaces for singularities with regular semi simple leading term. The new feature in our counting formulas is the appearance of characters of ...