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.