Affineness of the maximal \'{e}tale locus
Ivan Zelich
TL;DR
This paper proves a stronger version of the purity of the ramification locus theorem in algebraic geometry, using a Tor-independence result and tilting techniques over excellent regular local rings.
Contribution
It introduces a new Tor-independence result for étale schemes over regular local rings and applies tilting to perfect rings to strengthen the purity theorem.
Findings
Established a strong version of the purity of the ramification locus theorem.
Proved a Tor-independence result for étale schemes over excellent regular local rings.
Applied tilting to perfect rings to achieve the main results.
Abstract
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 sections of \'{e}tale schemes over excellent regular local rings, which we will prove by tilting to perfect rings.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Commutative Algebra and Its Applications · Algebraic structures and combinatorial models