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From SFB1085 - Higher Invariants
Jump to navigationJump to searchAbstract: Recently, Elmanto and Morrow gave a construction of motivic complexes for qcqs schemes. A basic idea coming from the trace method for algebraic K-theory, is to modify the cdh-local motivic complex (defined as the cdh sheafication of the left Kan extension of the motivic complex for smooth schemes over a field) by using other complexes such as Hodge completed derived de Rham complexes and syntomic complexes. In this talk, we propose a different construction of a motivic complex using a new Grothendieck topology, pro-cdh topology, and sketch a proof of the comparison theorem of two motivic complexes for Noetherian schemes over a field. This is a joint work with Shane Kelly.
