Sheela Devadas (UW)

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: https://washington.zoom.us/j/689897930

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