Algebraic Spaces and Stacks: Representabilty
We define what it means for a functor to be representable. We define what it means for a category to be representable.
From playlist Stacks
algebraic geometry 25 Morphisms of varieties
This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It covers the definition of a morphism of varieties and compares algebraic varieties with other types of locally ringed spaces.
From playlist Algebraic geometry I: Varieties
algebraic geometry 23 Categories
This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It gives a quick review of category theory as background for the definition of morphisms of algebraic varieties.
From playlist Algebraic geometry I: Varieties
Weil conjectures 7: What is an etale morphism?
This talk explains what etale morphisms are in algebraic geometry. We first review etale morphisms in the usual topology of complex manifolds, where they are just local homeomorphism, and explain why this does not work in algebraic geometry. We give a provisional definition of etale morphi
From playlist Algebraic geometry: extra topics
Schemes 10: Morphisms of affine schemes
This lecture is part of an online algebraic geometry course on schemes, based on chapter II of "Algebraic geometry" by Hartshorne. We try to define morphisms of schemes. The obvious definition as morphisms of ringed spaces fails as we show in an example. Instead we have to use the more su
From playlist Algebraic geometry II: Schemes
algebraic geometry 26 Affine algebraic sets and commutative rings
This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It covers the relation between morphisms of affine algebraic sets and homomorphisms of commutative rings. As examples it describes some homomorphisms of commutative rings
From playlist Algebraic geometry I: Varieties
Schemes 16: Morphisms of finite type
This lecture is part of an online algebraic geometry course on schemes, based on chapter II of "Algebraic geometry" by Hartshorne. We introduce three properties of morphisms: quasicompact, finite type, and locally of finite type, and give a few examples.
From playlist Algebraic geometry II: Schemes
Schemes 41: Morphisms to projective space
This lecture is part of an online course on algebraic geometry based on chapter II of "algebraic geometry" by Hartshorne. We discuss morphisms of a scheme to projective space, showing that they correspond to a line bundle with a set of sections generating it.
From playlist Algebraic geometry II: Schemes
Algebraic Spaces and Stacks: Definitions
We give the definition of algebraic stacks and spaces! Woot! I think algebraic spaces don't get enough love or stacks get too much love. I'm not sure which one... Algebraic Spaces: http://stacks.math.columbia.edu/tag/025X Algebraic Stacks: http://stacks.math.columbia.edu/tag/026N
From playlist Stacks
Algebraic Spaces and Stacks: Ideas
We try to give some motivation for the definitions we give in the subsequent videos.
From playlist Stacks
Vincent LAFFORGUE - Stacks of Shtukas and spectral decompositions
https://ams-ems-smf2022.inviteo.fr/
From playlist International Meeting 2022 AMS-EMS-SMF
A stacky approach to crystalline (and prismatic) cohomology - Vladimir Drinfeld
Joint IAS/Princeton University Number Theory Seminar Topic: A stacky approach to crystalline (and prismatic) cohomology Speaker: Vladimir Drinfeld Affiliation: The University of Chicago; Visiting Professor, School of Mathematics Date: October 3, 2019 For more video please visit http://vi
From playlist Mathematics
Equivariantization and de-equivariantization - Shotaro Makisumi
Geometric and Modular Representation Theory Seminar Topic: Equivariantization and de-equivariantization Speaker: Shotaro Makisumi Affiliation: Columbia University; Member, School of Mathematics Date: February 10, 2021 For more video please visit http://video.ias.edu
From playlist Seminar on Geometric and Modular Representation Theory
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
Sveta Makarova. Good moduli spaces for Artin stacks
Seminar talk on CORONA GS: https://murmuno.mit.edu/coronags Abstract: The talk is based on Alper's paper "Good moduli spaces for Artin stacks". I will briefly remind definitions of moduli problems and stacks and then proceed to explaining Alper's results. After that, I will focus on givin
From playlist CORONA GS
An algebro-geometric theory of vector-valued modular forms of half-integral weight - Luca Candelori
Luca Candelori Lousiana State University October 23, 2014 We give a geometric theory of vector-valued modular forms attached to Weil representations of rank 1 lattices. More specifically, we construct vector bundles over the moduli stack of elliptic curves, whose sections over the complex
From playlist Mathematics
Geordie Williamson: Langlands and Bezrukavnikov II Lecture 17
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 25: Proper morphisms and valuations
This lecture is part of an online algebraic geometry course on schemes, based on chapter II of "Algebraic geometry" by Hartshorne. We describe how to test a morphism for being proper using discrete valuation rings, and use this to show that projective morphisms are proper.
From playlist Algebraic geometry II: Schemes
The local-global principle for stacky curves - Poonen - Workshop 1 - CEB T2 2019
Bjorn Poonen (Massachusetts Institute of Technology) / 22.05.2019 The local-global principle for stacky curves For smooth projective curves of genus g over a number field, the local-global principle holds when g = 0 and can fail for g = 1, as has been known since the 1940s. Stacky curve
From playlist 2019 - T2 - Reinventing rational points