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?
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?
Who Gives a Sheaf? Part 2: A non-example
In this video we compare two pre-sheaves, one which is a sheaf, and one which is not.
From playlist Who Gives a Sheaf?
Schemes 42: Very ample sheaves
This lecture is part of an online algebraic geometry course on schemes, based on chapter II of "Algebraic geometry" by Hartshorne. We define ample and very ample invertible sheaves for projective varieties, and gives some examples for complex elliptic curves. We also show that some sect
From playlist Algebraic geometry II: Schemes
algebraic geometry 17 Affine and projective varieties
This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It covers the relation between affine and projective varieties, with some examples such as a cubic curve and the twisted cubic.
From playlist Algebraic geometry I: Varieties
Schemes 3: exactness and sheaves
This lecture is part of an online algebraic geometry course on schemes, based on chapter II of "Algebraic geometry" by Hartshorne. In it we discuss exactness of morphisms of sheaves over a topological space.
From playlist Algebraic geometry II: Schemes
Commutative algebra 43 (Stalkwise locally free 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 rather technical concept of stalkwise locally free modules: those such that all localizations at primes are fre
From playlist Commutative algebra
Schemes 48: The canonical sheaf
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 define the canonical sheaf, giev a survey of some applications (Riemann-Roch theorem, Serre duality, canonical embeddings, Kodaira dimensio
From playlist Algebraic geometry II: Schemes
Will Sawin - Bounding the stalks of perverse sheaves in characteristic p via the (...)
The sheaf-function dictionary shows that many natural functions on the F_q-points of a variety over F_q can be obtained from l-adic sheaves on that variety. To obtain upper bounds on these functions, it is necessary to obtain upper bounds on the dimension of the stalks of these sheaves. In
From playlist Franco-Asian Summer School on Arithmetic Geometry (CIRM)
Schemes 5: Definition of a scheme
This lecture is part of an online algebraic geometry course on schemes, based on chapter II of "Algebraic geometry" by Hartshorne. We give some historical background, then give the definition of a scheme and some simple examples, and finish by explaining the origin of the word "spectrum".
From playlist Algebraic geometry II: Schemes
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
Topological filters: a toolbox for processing dynamic signals - Michael Robinson
Workshop on Topology: Identifying Order in Complex Systems Topic: Topological filters: a toolbox for processing dynamic signals Speaker: Michael Robinson Affiliation: American University Date: April 7, 2018 For more videos, please visit http://video.ias.edu
From playlist Mathematics
This lecture is part of an online algebraic geometry course on schemes, based on chapter II of "Algebraic geometry" by Hartshorne. Given a continuous map between topological spaces there are two natural ways to transfer sheaves from one space to another. We summarize the main properties of
From playlist Algebraic geometry II: Schemes
This lecture is part of an online algebraic geometry course on schemes, based on chapter II of "Algebraic geometry" by Hartshorne. In it we explain why the obvious definition of an epimorphism of sheaves is wrong, and construct the etale space of a presheaf as preparation for giving the c
From playlist Algebraic geometry II: Schemes
Schemes 9: Spec R is a locally ringed space
This lecture is part of an online algebraic geometry course on schemes, based on chapter II of "Algebraic geometry" by Hartshorne. It gives the proof that the spectrum of a ring R is a locally ringed space, by checking the sheaf property.
From playlist Algebraic geometry II: Schemes
Commutative algebra 22 Flatness, tensor products, localization
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. In this lecture we introduce flat modules, show that R[1/S] is flat, and show that vanishing, flatness, and exactness are all
From playlist Commutative algebra
Schemes 32: The line bundles O(n) on projective space
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 construct a sheaf on a projective scheme Proj(R) from a graded module M over R, and use this to construct some line bundles O(n) on projective
From playlist Algebraic geometry II: Schemes
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
Schemes 34: Coherent sheaves on projective space
This lecture is part of an online algebraic geometry course on schemes, based on chapter II of "Algebraic geometry" by Hartshorne. This lecture discusses some of Serre's theorems about coherent sheaves on projective space. In particular we describe how coherent sheaves are related to finit
From playlist Algebraic geometry II: Schemes