Department of Mathematics
Ben Gurion University
Prof. Amnon Yekutieli
Department of Mathematics
Ben Gurion University
Prof. Amnon Yekutieli
(links to slides at bottom)
Title:
A DG Approach to the Cotangent Complex
Speaker:
Amnon Yekutieli, Ben Gurion University
Abstract: Let $B/A$ be a pair of commutative rings. We propose a DG (differential graded) approach to the cotangent complex $L_{B/A}$. Using a commutative semi-free DG ring resolution 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.
(abstract updated 2 April 2023)
Links to slides:
Lecture version 1 (BGU AG&NT seminar, 27 March 2023, title: An Algebraic Approach to the Cotangent Complex). slides (pdf), compact slides (pdf for printing)
Lecture version 2 (Paris algebra seminar, 3 April 2023). slides (pdf), compact slides (pdf for printing).
Lecture version 3 (Charles Univ. algebra seminar, 17 April 2023). slides (pdf), compact slides (pdf for printing).
Lecture version 4 (NDGTTC seminar, 23 May 2023). slides (pdf), compact slides (pdf for printing).
(page updated 19 Oct 2023)