Mon, August 31, 2020
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4:00pm [4:00pm] Chetan Balwe, IISER Mohali
Description:
Speaker: Chetan Balwe, IISER Mohali Time: Monday 31st August 4 to 5pm (joining time 3.50pm) Google Meet Link: https://meet.google.com/wnf-ywcy-ozi Title: Geometric approach for the sheaf of A^1-connected components Abstract: The $\mathbb{A}^1$-homotopy theory of Morel-Voevodsky attempts to use homotopical methods in algebraic geometry by having the affine line play the role of the unit interval. Analogous to the set of connected components of a topological space, one associates the sheaf of $\mathbb{A}^1$-connected components to any variety. However, this sheaf is extremely difficult to compute since its definition is mired in abstract machinery. We will discuss how this sheaf may be studied by means using purely algebro-geometric methods, via the sheaf of ``naively" $\mathbb{A}^1$-connected components. This approach has been successful in proving some results about the sheaf of $\mathbb{A}^1$-connected components by very elementary techniques. We will look at some of these results and briefly describe the techniques used to prove them. This talk is based on joint work with Amit Hogadi and Anand Sawant.

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