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math.AG2026
The Miracle of Flatness in Algebraic Geometry
Ivan Zelich
This thesis studies various aspects of flatness in algebraic geometry. We first study flatness in the context of semi-rings. We prove some discreteness results for a derived groupi…
math.AG2026
Affineness of the maximal étale locus
Ivan Zelich
In this paper we will prove a strong version of the celebrated purity of the ramification locus theorem in algebraic geometry. Our key input is a Tor-independence result for global…