Featured Speaker:  Niven Achenjang (MIT)

Title:  Flat, smooth, and étale morphisms

Abstract:  References: Mumford, The red book of varieties and schemes, III.5 and III.10; or Poonen, Rational points on varieties, Sections 3.3 and 3.5.

Smooth varieties give an algebraic analogue of (smooth) manifolds from differential geometry, while smooth and étale morphisms give algebraic analogues of submersions and local isomorphisms. In addition to translating important notions from differential geometry into the algebraic setting, maps of these types play an important role in later development of étale cohomology. In this talk, we will introduce the definitions and basic properties of smooth and étale morphisms with an emphasis on providing intuition for thinking about them.

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