# Overconvergent Homotopy Invariant Presheaves with Transfers over Smooth Rigid Varieties

 MOTIVIC COHOMOLOGY Topic: Overconvergent Homotopy Invariant Presheaves with Transfers over Smooth Rigid Varieties Speaker: Joseph Ayoub Affiliation: Université Paris 7, France and Member, School of Mathematics Date: Thursday, April 12 Time/Room: 11:00am - 12:00pm/S-101

Let F be a presheaf with transfers on the category of smooth affinoid varieties over a non-archemidean field. Suppose that F is overconvergent and homotopy invariant. Then the presheaves H^i(-,F) are also homotopy invariant (where the cohomology is taken for the Nisnevich or the usual topology). Moreover, the restriction of F to the small site of the Tate Ball is already a sheaf with zero higher cohomology groups.