Schemes 17: Finite, quasifinite
This lecture is part of an online algebraic geometry course on schemes, based on chapter II of "Algebraic geometry" by Hartshorne. We define finite morphisms, and attempt to sort out the three different definition of quasifinite morphisms in the literature.
From playlist Algebraic geometry II: Schemes
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
This lecture is part of an online algebraic geometry course on schemes, based on chapter II of "Algebraic geometry" by Hartshorne.. We define proper morphisms in topology and geometry, and show that finite morphisms are proper.
From playlist Algebraic geometry II: Schemes
We give a buttload of definitions for morphisms on various categories of complexes. The derived category of an abelian category is a category whose objects are cochain complexes and whose morphisms I describe in this video.
From playlist Derived Categories
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 15: Quasicompact, Noetherian
This lecture is part of an online algebraic geometry course on schemes, based on chapter II of "Algebraic geometry" by Hartshorne. We define quasi-compact, Noetherian, and locally Noetherian schemes, give a few examples, and show that "locally Noetherian" is a local property.
From playlist Algebraic geometry II: Schemes
Schemes 21: Separated morphisms
This lecture is part of an online algebraic geometry course on schemes, based on chapter II of "Algebraic geometry" by Hartshorne.. We define separated and quasi-separated schemes and morphisms, give a few examples, and show that if a scheme has a separated morphism to an affine scheme the
From playlist Algebraic geometry II: Schemes
Math 101 Fall 2017 112917 Introduction to Compact Sets
Definition of an open cover. Definition of a compact set (in the real numbers). Examples and non-examples. Properties of compact sets: compact sets are bounded. Compact sets are closed. Closed subsets of compact sets are compact. Infinite subsets of compact sets have accumulation poi
From playlist Course 6: Introduction to Analysis (Fall 2017)
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
Math 131 092816 Continuity; Continuity and Compactness
Review definition of limit. Definition of continuity at a point; remark about isolated points; connection with limits. Composition of continuous functions. Alternate characterization of continuous functions (topological definition). Continuity and compactness: continuous image of a com
From playlist Course 7: (Rudin's) Principles of Mathematical Analysis
This lecture is part of an online algebraic geometry course on schemes, based on chapter II of "Algebraic geometry" by Hartshorne. We define open and closed immersion, and give some basic properties and some examples.
From playlist Algebraic geometry II: Schemes
Winter School JTP: Introduction to A-infinity structures, Bernhard Keller, Lecture 3
In this minicourse, we will present basic results on A-infinity algebras, their modules and their derived categories. We will start with two motivating problems from representation theory. Then we will briefly present the topological origin of A-infinity structures. We will then define and
From playlist Winter School on “Connections between representation Winter School on “Connections between representation theory and geometry"
C. Leininger - Teichmüller spaces and pseudo-Anosov homeomorphism (Part 1)
I will start by describing the Teichmuller space of a surface of finite type from the perspective of both hyperbolic and complex structures and the action of the mapping class group on it. Then I will describe Thurston's compactification of Teichmuller space, and state his classification
From playlist Ecole d'été 2018 - Teichmüller dynamics, mapping class groups and applications
Virtual rigid motives of definable sets in valued fields - A. Forey - Workshop 2 - CEB T1 2018
Arthur Forey (Sorbonne Université) / 08.03.2018 Virtual rigid motives of definable sets in valued fields. In an instance of motivic integration, Hrushovski and Kazhdan study the definable sets in the theory of algebraically closed valued fields of characteristic zero. They show that the
From playlist 2018 - T1 - Model Theory, Combinatorics and Valued fields
Drinfeld's lemma for schemes - Kiran Kedlaya
Joint IAS/Princeton University Algebraic Geometry Seminar Topic: Drinfeld's lemma for schemes Speaker: Kiran Kedlaya Affiliation: University of California, San Diego; Visiting Professor, School of Mathematics Date: February 4, 2019 For more video please visit http://video.ias.edu
From playlist Joint IAS/PU Algebraic Geometry
Ana Caraiani - 3/3 Shimura Varieties and Modularity
We discuss vanishing theorems for the cohomology of Shimura varieties with torsion coefficients, under a genericity condition at an auxiliary prime. We describe two complementary approaches to these results, due to Caraiani-Scholze and Koshikawa, both of which rely on the geometry of the H
From playlist 2022 Summer School on the Langlands program
Danny Calegari: Big Mapping Class Groups - lecture 4
Part I - Theory : In the "theory" part of this mini-course, we will present recent objects and phenomena related to the study of big mapping class groups. In particular, we will define two faithful actions of some big mapping class groups. The first is an action by isometries on a Gromov-h
From playlist Topology
Math 131 Fall 2018 100318 Heine Borel Theorem
Definition of limit point compactness. Compact implies limit point compact. A nested sequence of closed intervals has a nonempty intersection. k-cells are compact. Heine-Borel Theorem: in Euclidean space, compactness, limit point compactness, and being closed and bounded are equivalent
From playlist Course 7: (Rudin's) Principles of Mathematical Analysis (Fall 2018)