Rutger NootAbelian varieties, Mumford–Tate groups and representations of Weil–Deligne groups.
On Friday 07–07–2017.

Let A be an abelian variety defined over a number field F. We can associate to A its Mumford–Tate group G (an algebraic group over Q) and a system of l-adic Galois representations. Up to a finite extension of F, each l-adic representation factors through G(Ql). I will discuss to what extend these representations for a compatible system with values in G. This requires taking the restriction of the system to the decomposition group of any valuation v of F and the study of the corresponding system of representations (with values in G) of the Weil–Deligne group of Fv. I will concentrate on the case where A has bad (semistable) reduction at v and on the way the p-adic representation fits into the system (p being the residue characteristic at v).