Derived-tame blowing-up of tree algebras

Blowing up Feynman integrals

In this talk we discuss sector decomposition. This is a method to disentangle overlapping singularities through a sequence of blow-ups. We report on an open-source implementation of this algorithm to compute numerically the Laurent expansion of divergent multi-loop integrals. We also show how this method can be used to prove a theorem which relates the coefficients of the Laurent series of dime...

Section 2.7.1 - Blowing Up

Now we come to the generalised notion of blowing up. In (I, §4) we defined the blowing up of a variety with respect to a point. Now we will define the blowing up of a noetherian scheme with respect to any closed subscheme. Since a closed subscheme corresponds to a coherent sheaf of ideals, we may as well speak of blowing up a coherent sheaf of ideals. The necessary background for this section i...

On Ringel-hall Algebras of Tame Hereditary Algebras

Derivations of UP-algebras by means of UP-endomorphisms

The notion of $f$-derivations of UP-algebras is introduced, some useful examples are discussed, and related properties are investigated. Moreover, we show that the fixed set and the kernel of $f$-derivations are UP-subalgebras of UP-algebras,and also give examples to show that the two sets are not UP-ideals of UP-algebras in general.

Subfields of Nondegenerate Tame Semiramified Division Algebras

We show in this article that in many cases the subfields of a nondegenerate tame semiramified division algebra of prime power degree over a Henselian valued field are inertial field extensions of the center [Th. 2.5, Th. 2.12 and Prop. 2.16 ].