11:30 → 12:20 - Rational Points On Linear Algebraic Groups
In 1984, Oesterlé proved that a wound unipotent group of dimension strictly less than p -1 over a global function field of characteristic p has only finitely many rational points. The bound p -1 is sharp, as one can construct wound unipotent groups of dimension p -1 which are unirational and therefore have Zariski dense sets of rational points. Oesterle posed the natural question: Must a wound unipotent group over a global function field which admits infinitely many rational points admit a nontrivial unirational subgroup? One can of course formulate the question for arbitrary linear algebraic groups (though the wound unipotent case turns out to be the crucial one).
In this talk, I will discuss a proof of the affirmative answer to Oesterlé's question (in this slightly greater generality).
Speaker : Zev ROSENGARTEN
15:00 → 15:50 - Simple Modules for Algebraic Groups
I will speak about joint work with David Stewart, giving a classification by highest weight of simple modules for smooth connected algebraic groups over a field, and also describe some of the properties of those modules. Much of the work here shows the fundamental influence of Tits: our work relies on work of Conrad-Gabber-Prasad classifying pseudo-reductive groups, which in turn (pseudo-)completed a program initiated by Tits in the 1990s. Further, in moving from the split to the non-split case, and in calculating the endomorphisms of the simple modules, we also mimic work of Tits from the 1970s for reductive groups.
Speaker : Michael BATE
16:00 → 16:50 - Higher Tate Traces and Classification of Chow Motives
This talk is based on a joint work with Charles De Clercq. The main result is a classification theorem for some Chow motives with finite coefficients, which applies, notably, to motives of projective homogeneous varieties under some semisimple algebraic groups. The result uses a new invariant, the Tate trace of a motive, defined as a pure Tate summand of maximal rank. If time permits, the notion of critical variety, related to the Tits index of the underlying algebraic group, will be presented, as an application of our result.
Speaker : Anne QUÉGUINER-MATHIEU
