Mon, August 31, 2020
Public Access Category: All |
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- Time:
- 4:00pm-5:00pm
- 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.