Eoin Mackall | Pro-representability of some K-cohomology groups
Channel: EIMI, PDMI RAS and Chebyshev Laboratory
Date: 2022-04-27

Seminar on A1-topology, motives and K-theory, April 27, 2022
Eoin Mackall (University of Maryland)
Pro-representability of some K-cohomology groups

Representability of the Chow groups of a variety typically fails outside the case of codimension-1 cycles (often for somewhat trivial reasons). In 1975, Bloch studied the question of representability for codimension-2 cycles and proved the (weaker) result that appropriate K-cohomology groups were pro-representable for varieties defined over a number field and with hodge numbers vanishing in certain degrees. Using recent work of others, we revisit this result and explain how it can be extended to prove pro-representability for K-cohomology groups related to codimension-3 cycles for some varieties over number fields whose hodge numbers satisfy some more general vanishing constraints.