On the intersection motive of certain Shimura varieties: the case of Siegel threefolds

In this article, we construct a Hecke-equivariant Chow motive whose realizations equal intersection cohomology of Siegel threefolds with regular algebraic coefficients. As a consequence, we are able to define Grothendieck motives for Siegel modular forms.Comment: 36 pages; accepted for publication in Annals of K-Theory. Following remarks of the referee, the proof of Cor. 1.13 is now more detaile

On the interior motive of certain Shimura varieties: the case of Picard surfaces

The purpose of this article is to construct a Hecke-equivariant Chow motive whose realizations equal interior (or intersection) cohomology of Picard surfaces with regular algebraic coefficients. As a consequence, we are able to define Grothendieck motives for Picard modular forms.Comment: 34 pages; accepted for publication in manuscripta mathematica. arXiv admin note: text overlap with arXiv:0906.423

The boundary motive: definition and basic properties

We introduce the notion of the boundary motive of a scheme X over a perfect field. By definition, it measures the difference between the motive X and the motive with compact support of X. We develop three tools to compute the boundary motive in terms of the geometry of a compactification of X: co-localization, invariance under abstract blow-up, and analytical invariance. We then prove auto-duality of the boundary motive of a smooth scheme X. As a formal consequence of this, and of co-localization, we obtain a fourth computational tool, namely localization for the boundary motive.Comment: 33 pages; accepted for publication in Comp. Math. Following the request of the referee, a section on the case of normal crossings was adde

On the interior motive of certain Shimura varieties: the case of Hilbert-Blumenthal varieties

The purpose of this article is to construct a Hecke-equivariant Chow motive whose realizations equal interior (or intersection) cohomology of Hilbert-Blumenthal varieties with non-constant algebraic coefficients.Comment: 31 pages; no changes wrt. last version except for the numbering of the sections, which is now compatible with the published versio

Phase diagram and critical properties in the Polyakov--Nambu--Jona-Lasinio model

We investigate the phase diagram of the so-called Polyakov--Nambu--Jona-Lasinio model at finite temperature and nonzero chemical potential with three quark flavours. Chiral and deconfinement phase transitions are discussed, and the relevant order-like parameters are analyzed. The results are compared with simple thermodynamic expectations and lattice data. A special attention is payed to the critical end point: as the strength of the flavour-mixing interaction becomes weaker, the critical end point moves to low temperatures and can even disappear.Comment: Talk given at the 9th International Conference on Quark Confinement and the Hadron Spectrum - QCHS IX, Madrid, Spain, 30 August - September 201