Motivic invariants of quivers via dimensional reduction

Motivic construction of cohomological invariants

The norm varieties and the varieties with special correspondences play a major role in the proof of the Bloch-Kato Conjecture by M. Rost and V. Voevodsky. In the present paper we show that a variety which possesses a special correspondence is a norm variety. As an unexpected application we give a positive answer to a problem of J.-P. Serre about groups of type E8 over Q. Apart from this we incl...

Motivic Invariants of Algebraic Tori

We prove a trace formula and a global form of Denef and Loeser’s motivic monodromy conjecture for tamely ramified algebraic tori over a discretely valued field. If the torus has purely additive reduction, the trace formula gives a cohomological interpretation for the number of components of the Néron model.

Invariants of Mixed Representations of Quivers I

Semi-invariants of 2-representations of Quivers

In this work we obtain a version of the Procesi-Rasmyslov Theorem for the algebra of semi-invariants of representations of an arbitrary quiver with dimension vector (2, 2, . . . , 2).

Semi-invariants of mixed representations of quivers

The notion of mixed representations of quivers can be derived from ordinary quiver representations by considering the dual action of groups on “vertex” vector spaces together with the usual action. A generating system for the algebra of semi-invariants of mixed representations of a quiver is determined. This is done by reducing the problem to the case of bipartite quivers of the special form an...