Naive $\mathbb A^1$-homotopies on surfaces

Abstract: We will describe an algebraic criterion for two morphisms of the spectrum of a henselian regular local ring into a smooth projective surface to be naively $\mathbb A^1$-homotopic. If time permits, we will explain the significance of this criterion to purely algebro-geometric questions related to $\mathbb A^1$-connected components. The talk is based on joint work with Chetan Balwe.

Mathematics

Audience: advanced learners

IIT Bombay Virtual Commutative Algebra Seminar

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