A venue for invited and local speakers to present their research on topics surrounding algebraic geometry and number theory, broadly conceived. All meetings start at 16:00 sharp and end at 17:00. Some meetings are held in the subterranean room -101, others are held online. We expect to broadcast most meetings over Zoom at the URL https://us02web.zoom.us/j/84396320442
The seminar meets on Mondays, 12:10-13:10, in -101
Let $B/A$ be a pair of commutative rings. We propose an algebraic approach to the cotangent complex $L_{B/A}$. Using commutative semi-free DG ring resolutions of B relative to A, we construct a complex of $B$-modules $LCot_{B/A}$. This construction works more generally for a pair $B/A$ of commutative DG rings.
In the talk we will explain all these concepts. Then we will discuss the important properties of the DG $B$-module $LCot_{B/A}$. It time permits, we’ll outline some of the proofs.
It is conjectured that for a pair of rings $B/A$, our $LCot_{B/A}$ coincides with the usual cotangent complex $L_{B/A}$, which is constructed by simplicial methods. We shall also relate $LCot_{B/A}$ to modern homotopical versions of the cotangent complex.