Combinatorics of the basic stratum

We express the cohomology of the basic stratum of some unitary Shimura varieties associated to division algebras in terms of automorphic representations of the group in the Shimura datum

The trace formula and the existence of PEL type Abelian varieties modulo p

We show, using the trace formula, that any Newton stratum of a Shimura variety of PEL-type of types (A) and (C) is non-empty at the primes of good reduction. Furthermore we prove conditionally the non-emptiness for Shimura data associated to odd Spin groups. Our results are conditional on Rapoport-Langlands conjecture and Arthur's conjectures on the discrete spectrum. Both these results have been announced by Arthur and Kisin in significant cases

Hic situs est: occupational identity of Roman jewelers

In their grave inscriptions craftsmen – or their living relatives – mentioned their occupation and other aspects of their identity: the location of their workshop, supporting their former slaves as a patronus and being a member of/having a function in a collegium. However, they did not mention their skills. Craftsmen chose to show how successful they were, because they had to earn enough money to be able to do all this. This way they created an identity of individual financial success that fits the elite ideal of economic identity. This created identity gave the craftsmen social status

The basic stratum of some simple Shimura varieties

Under simplifying hypotheses we prove a relation between the l-adic cohomology of the basic stratum of a Shimura variety of PEL-type modulo a prime of good reduction of the reflex field and the cohomology of the complex Shimura variety. In particular we obtain explicit formulas for the number of points in the basic stratum over finite fields. We obtain our results using the trace formula and truncation of the formula of Kottwitz for the number of points on a Shimura variety over a finite fields.Comment: Corrected and updated versio

Men fear other men most: Gender specific brain activations in perceiving threat from dynamic faces and bodies. An fMRI study.

We report a functional magnetic resonance imaging experiment showing different activation patterns as a function of threatening signals from facial or bodily expressions and these differed between male and female participants as a function of male and female actors. Male observers showed a clear motor preparation response to threatening male body language