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Morphisms and cohomology comparison for Henselian schemes

Sheela Devadas (UW)
Tuesday, November 2, 2021 - 2:00pm
PDL C-38
Preseminar 2-2:30
Title: Henselian pairs
Abstract: The global analogue of a Henselian local ring is a Henselian pair - i.e., a ring R and an ideal I which satisfy a condition resembling Hensel's lemma regarding lifting coprime factorizations of polynomials over R/I to factorizations over R. I will discuss various definitions of Henselian pairs, as well as related notions like Henselization and Artin-Popescu approximation which are useful for working with Henselian schemes.
Seminar 2:30-3:30
Title: Morphisms and cohomology comparison for Henselian schemes
Abstract: The geometric counterpart of a Henselian pair is the notion of Henselian schemes, which can serve as an ``algebraic'' substitute for formal schemes in applications such as deformation theory. In this talk I will discuss Henselian schemes and quasi-coherence, and will also develop the theory of smooth and étale morphisms of Henselian schemes. Finally, I prove a GAGA-style cohomology comparison result for Henselian schemes in positive characteristic, and discuss algebraizability of coherent sheaves on the Henselization of a proper scheme.
The talk will also be available via Zoom:
password: etale-site
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