Who Gives a Sheaf? Part 1: A First Example
We take a first look at (pre-)sheaves, as being inspired from first year calculus.
From playlist Who Gives a Sheaf?
This lecture is part of an online algebraic geometry course on schemes, based on chapter II of "Algebraic geometry" by Hartshorne. We define coherent modules over rings and coherent sheaves, and then discuss when the amps f* and f_* preserve coherence or quasicoherence.
From playlist Algebraic geometry II: Schemes
What is a Module? (Abstract Algebra)
A module is a generalization of a vector space. You can think of it as a group of vectors with scalars from a ring instead of a field. In this lesson, we introduce the module, give a variety of examples, and talk about the ways in which modules and vector spaces are different from one an
From playlist Abstract Algebra
Who Gives a Sheaf? Part 3: Mighty Morph'n Morphisms
In this video we discuss the definition of a morphism of sheaves.
From playlist Who Gives a Sheaf?
This lecture is part of an online course on rings and modules. We mainly discuss the problem of whether free modules over a ring have a well defined ran, generalizing the dimension of a vector space. We show that they do over many rings, including all non-zero commutative rings, but give
From playlist Rings and modules
0:00 Motivation for studying modules 4:45 Definition of a vector space over a field 9:31 Definition of a module over a ring 12:12 Motivating example: structure of abelian groups 16:05 Motivating example: Jordan normal form 19:44 What unifies both examples (spoiler): Structure theorem for f
From playlist Abstract Algebra 2
Rings and modules 2: Group rings
This lecture is part of an online course on rings and modules. We decribe some examples of rings constructed from groups and monoids, such as group rings and rings of Dirichlet polynomials. For the other lectures in the course see https://www.youtube.com/playlist?list=PL8yHsr3EFj52XDLrm
From playlist Rings and modules
Commutative algebra 42 Projective modules
This lecture is part of an online course on commutative algebra, following the book "Commutative algebra with a view toward algebraic geometry" by David Eisenbud. We discuss the relation between locally free things (vector bundles) and projective things. In commutative algebra and differe
From playlist Commutative algebra
From Cohomology to Derived Functors by Suresh Nayak
PROGRAM DUALITIES IN TOPOLOGY AND ALGEBRA (ONLINE) ORGANIZERS: Samik Basu (ISI Kolkata, India), Anita Naolekar (ISI Bangalore, India) and Rekha Santhanam (IIT Mumbai, India) DATE & TIME: 01 February 2021 to 13 February 2021 VENUE: Online Duality phenomena are ubiquitous in mathematics
From playlist Dualities in Topology and Algebra (Online)
Rings 12 Duality and injective modules
This lecture is part of an online course on rings and modules. We descibe some notions of duality for modules generalizing the dual of a vector space. We first discuss duality for free and projective modules, which is very siilar to the vector space case. Then we discuss duality for finit
From playlist Rings and modules
Schemes 27: Quasicoherent sheaves
This lecture is part of an online algebraic geometry course on schemes, based on chapter II of "Algebraic geometry" by Hartshorne. We show how to turn a module over a ring into a sheaf of modules over its spectrum. A quasicoherent sheaf of modules of one which looks locally like one constr
From playlist Algebraic geometry II: Schemes
Geordie Williamson: Langlands and Bezrukavnikov II Lecture 16
SMRI Seminar Series: 'Langlands correspondence and Bezrukavnikov’s equivalence' Geordie Williamson (University of Sydney) Abstract: The second part of the course focuses on affine Hecke algebras and their categorifications. Last year I discussed the local Langlands correspondence in bro
From playlist Geordie Williamson: Langlands correspondence and Bezrukavnikov’s equivalence
Schemes 45: Blowing up schemes
This lecture is part of an online algebraic geometry course on schemes, based on chapter II of "Algebraic geometry" by Hartshorne. In this lecture we discuss the operation of blowing up a scheme along a sheaf of ideals. This can be used to make ideals invertible, and to eliminate points o
From playlist Algebraic geometry II: Schemes
Matthew Morrow: Relative integral p-adic Hodge theory
Abstract: Given a smooth scheme X over the ring of integers of a p-adic field, we introduce the notion of a relative Breuil-Kisin-Fargues module M on X. Each such M simultaneously encodes the data of a lisse étale sheaf, a module with flat connection, and a crystal, whose cohomologies are
From playlist Algebraic and Complex Geometry
Marc Levine: The rational motivic sphere spectrum and motivic Serre finiteness
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist SPECIAL 7th European congress of Mathematics Berlin 2016.
Duality in Algebraic Geometry by Suresh Nayak
PROGRAM DUALITIES IN TOPOLOGY AND ALGEBRA (ONLINE) ORGANIZERS: Samik Basu (ISI Kolkata, India), Anita Naolekar (ISI Bangalore, India) and Rekha Santhanam (IIT Mumbai, India) DATE & TIME: 01 February 2021 to 13 February 2021 VENUE: Online Duality phenomena are ubiquitous in mathematics
From playlist Dualities in Topology and Algebra (Online)
Finiteness, Z_l-sheaves
From playlist Étale cohomology and the Weil conjectures
Schemes 28: Examples of quasicoherent sheaves
This lecture is part of an online algebraic geometry course on schemes, based on chapter II of "Algebraic geometry" by Hartshorne. We give some examples of quasicoherent sheaves over affine schemes, and define vector bundles, line bundles, and the Picard group.
From playlist Algebraic geometry II: Schemes
Introduction and Derivation of F[x]-Modules
Modules over a polynomial ring have very important applications to linear algebra. Here we prove some basic properties of F[x]-modules and show how they are related to vector spaces over a field. Ring & Module Theory playlist: https://www.youtube.com/playlist?list=PLug5ZIRrShJExMapwnaKTFX
From playlist Ring & Module Theory