Cohomology theories in the moduli of ring stacks
Abstract
We show that the natural map from the syntomification of a ring R to the stack of R-algebra stacks is fully faithful, answering a question of Drinfeld, and we describe its essential image in terms of underlying monoid stacks. We also give similar statements in the characteristic 0 filtered de Rham, = p \'etale, and Betti settings.
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