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On Postnikov completeness for replete topoi

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arxiv 2210.14146 v2 pith:IQCDQQBA submitted 2022-10-25 math.AT math.AG

Shubhodip Mondal , Emanuel Reinecke This is my paper · ORCID
classification math.ATmath.AG
keywords repletepostnikovtopoitoposaffineansweringassociatedbhatt
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abstract

We show that the hypercomplete $\infty$-topos associated with any replete topos is Postnikov complete, positively answering a question of Bhatt and Scholze; this will be deduced from the Milnor sequences for sheaves of spaces on replete topoi that we construct. As a corollary, we generalize a result of To\"en on affine stacks.

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  1. A 6-functor formalism for solid quasi-coherent sheaves on the Fargues-Fontaine curve

    math.AG 2024-12 accept novelty 7.0 of 10

    A 6-functor formalism for Z_p-linear solid quasi-coherent sheaves on small v-stacks is constructed, yielding Poincare duality for pro-etale Q_p-cohomology.

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