3 papers
math.AG2024
A pro-cdh topology on formal schemes
Shane Kelly, Shuji Saito
We introduce a pro-cdh topology on formal schemes and prove that the -topos of pro-cdh sheaves of spaces has an optimal bound of homotopy dimension. This remedies a defect…
math.KT2024
On pro-cdh descent on derived schemes
Shane Kelly, Shuji Saito, Georg Tamme
Grothendieck's formal functions theorem states that the coherent cohomology of a Noetherian scheme can be recovered from that of a blowup and the infinitesimal thickenings of the c…
math.AG2024
A procdh topology
Shane Kelly, Shuji Saito
In this article we propose a definition of a procdh topos. We show that it encodes procdh excision, has bounded homotopy dimension and therefore is hypercomplete and admits a conse…