Pro-representability of some K-cohomology groups

by Eoin Mackall (University of Maryland)

Wednesday 27 Apr 2022, 16:00 → 18:00 Europe/Moscow

818-1526-4739 (Zoom)

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.

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