On extension of the motivic cohomology beyond smooth schemes

Abstract

We construct an algebraic-cycle based model for the motivic cohomology on the category of schemes of finite type over a field, where schemes may admit arbitrary singularities and may be non-reduced. We show that our theory is functorial on the category, that it detects nilpotence, and that its restriction to the subcategory of smooth schemes agrees with the pre-existing motivic cohomology theory, which is the higher Chow theory of S. Bloch (Adv. Math., 1986). A few structures and applications are discussed.

v2: 104 pages. Minor updates. The topological support requirement for cycles and some relevant parts removed, because it holds always

References in corpus (6)

• Higher Topos Theory
• Algebraic cobordism
• Motives with modulus
• A moving lemma for algebraic cycles with modulus and contravariance
• Integral Regulators for Higher Chow Complexes
• Bertini theorems for hypersurface sections containing a subscheme over finite fields