Derived algebraic geometry and Shimura varieties: Tue, Th 11am-12pm
Zoom link: https://bccte.zoom.us/j/93757766454
Lecture 1: How to produce infinity categories? Video
Lecture 2: Functor categories and the Yoneda lemma Video
Lecture 3: Animation Video
Lecture 4: Animated commutative algebra Video
Lecture 5: The cotangent complex and deformation theory Video
Lecture 6: Obstruction theory and tangent spaces of mapping prestacks Video
Lecture 7: Deformations of maps between abelian schemes Video
Lecture 8: Derived homomorphisms between abelian schemes Video '
Lecture 9: A quasi-smooth scheme of homomorphisms of abelian schemes Video
Lecture 10: Quasi-smooth subschemes and cycle classes Video
Lurie, Higher Topos Theory : This is the most complete reference for the basic theory of infinity categories, though of course it's quite the chunky morsel.
Lurie, Higher Algebra : Here is where you'll find the basics of stable infinity categories (with a complete proof of the Dold-Kan correspondence), as well as all the gory details behind symmetric monoidal infinity categories and commutative algebra objects in such.
Cisinski, Higher categories and homotopical algebra : A more accessible and somewhat different perspective than Lurie's on the construction and properties of infinity categories.
Mazel-Gee, A user's guide to co/cartesian fibrations : A nice primer on how the Grothendieck construction works, and how it generalizes to the infinity category theoretic context.
Mazel-Gee, UC Berkeley Thesis : The introductory Chapter 0 of this thesis is very well-written and lays out the general paradigm of infinity categorical thinking, albeit in sometimes amusingly breathless terms.
Mao, Revisiting derived crystalline cohomology : A very clear exposition of how the process of animation works as well as how to make calculations in it.
Khan, Descent in algebraic K-theory : The first few lectures here give a nice exposition of the basics of derived algebraic geometry