Equivalence (mathematics) | Algebraic geometry

Adequate equivalence relation

In algebraic geometry, a branch of mathematics, an adequate equivalence relation is an equivalence relation on algebraic cycles of smooth projective varieties used to obtain a well-working theory of such cycles, and in particular, well-defined intersection products. Pierre Samuel formalized the concept of an adequate equivalence relation in 1958. Since then it has become central to theory of motives. For every adequate equivalence relation, one may define the category of pure motives with respect to that relation. Possible (and useful) adequate equivalence relations include rational, algebraic, homological and numerical equivalence. They are called "adequate" because dividing out by the equivalence relation is functorial, i.e. push-forward (with change of codimension) and pull-back of cycles is well-defined. Codimension 1 cycles modulo rational equivalence form the classical group of divisors modulo linear equivalence. All cycles modulo rational equivalence form the Chow ring. (Wikipedia).

Video thumbnail

12 Equivalence relations

Put all three properties of binary relations together and you have an equivalence relation.

From playlist Abstract algebra

Video thumbnail

Set Theory (Part 6): Equivalence Relations and Classes

Please feel free to leave comments/questions on the video and practice problems below! In this video, I set up equivalence relations and the canonical mapping. The idea of equivalence relation will return when we construct higher-level number systems, e.g.integers, from the natural number

From playlist Set Theory by Mathoma

Video thumbnail

Equivalence Relations Definition and Examples

Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Equivalence Relations Definition and Examples. This video starts by defining a relation, reflexive relation, symmetric relation, transitive relation, and then an equivalence relation. Several examples are given.

From playlist Abstract Algebra

Video thumbnail

Equivalence Relations!

This video is a full introduction to equivalence relations. Timestamps: 0:00 What is a relation? 3:02 Terminology - A Relation defined on a Set 4:02 Equivalence Relation Definition 7:18 Reflexive 9:18 Symmetric 11:48 Transitive Thanks for watching! Comment below with questions, and make

From playlist Proofs

Video thumbnail

Univalent foundations and the equivalence principle - Benedikt Ahrens

Short Talks by Postdoctoral Members Benedikt Ahrens - September 21, 2015 http://www.math.ias.edu/calendar/event/88134/1442858400/1442859300 More videos on http://video.ias.edu

From playlist Short Talks by Postdoctoral Members

Video thumbnail

L2.2. Equivalence relations

The picture in the lecture was taken from Wikipedia: https://en.wikipedia.org/wiki/Demographics_of_the_United_States#/media/File:USA2020dec1.png

From playlist Abstract Algebra 1

Video thumbnail

Discrete Math - 9.5.1 Equivalence Relations

Exploring a special kind of relation, called an equivalence relation. Equivalence classes and partitions are also discussed. Textbook: Rosen, Discrete Mathematics and Its Applications, 7e Playlist: https://www.youtube.com/playlist?list=PLl-gb0E4MII28GykmtuBXNUNoej-vY5Rz

From playlist Discrete Math I (Entire Course)

Video thumbnail

Choice Functions and Length: Why you can't measure everything you choose

I haven't talked about the axiom of choice in a while, and the relationship between choice functions and length (or size) and why you can't measure everything you choose seemed like a good way to do so. The interplay between choice functions and how one can construct sets for which measure

From playlist The New CHALKboard

Video thumbnail

9. Linguistics and Literature

Introduction to Theory of Literature (ENGL 300) In this lecture on the work of Roman Jakobson, Professor Paul Fry continues his discussion of synchrony and diachrony. The relationships among formalism, semiotics, and linguistics are explored. Claude Levi-Strauss's structural interpretat

From playlist Introduction to Theory of Literature with Paul H. Fry

Video thumbnail

A. J. Ayer on the Concept of a Person (1961)

In this talk, A. J. Ayer explores mind-body issues and that of personal identity. What is it that makes you who you are? Physical features of your body? Mental features of the mind? A combination of the two? If scientists could transfer all of your mental contents to another body, would yo

From playlist Philosophy of Mind

Video thumbnail

Stanford Seminar - On the Origin of Experience: The Shaping of Sense and the Complex World

"On the Origin of Experience: The Shaping of Sense and the Complex World" -Steven Ericsson-Zenith Colloquium on Computer Systems Seminar Series (EE380) presents the current research in design, implementation, analysis, and use of computer systems. Topics range from integrated circuits to

From playlist Engineering

Video thumbnail

Equivalences and Partitions, Axiomatic Set Theory 2 2

Defining equivalences and partitions of sets, and proving some theorems about their relations to each other. My Twitter: https://twitter.com/KristapsBalodi3 Equivalence Relations:(0:00) Partitions:(9:22) Connecting Equivalence and Partitions:(14:09) Representatives:(27:04)

From playlist Axiomatic Set Theory

Video thumbnail

(Part 2) The Palamite Controversy: A Thomistic Analysis by Fr. Peter Totleben, O.P.

A reading of chapter 2 (God and His Activity in the World: A Thomistic Approach) of "The Palamite Controversy: A Thomistic Analysis" by Peter Totleben, O.P. https://www.academia.edu/35580908/The_Palamite_Controversy_A_Thomistic_Analysis

From playlist Palamas and Thomism

Video thumbnail

What do we mean by "equal" - Pierre Deligne

Vladimir Voevodsky Memorial Conference Topic: What do we mean by "equal" Speaker: Pierre Deligne Affiliation: Professor Emeritus, School of Mathematics Date: September 11, 2018 For more video please visit http://video.ias.edu

From playlist Mathematics

Video thumbnail

Two Equivalence Classes [a] and [b] Are Equal If and Only If a is Related to b

In this video I prove a statement surrounding relations. We have an equivalence relation on a set A and we have to show that the equivalence class of a is equal to the equivalence class of b if and only if a is related to b. If you enjoyed this video please consider liking, sharing, and

From playlist Relations

Video thumbnail

Automorphy Lifting for Galois Representations With Small Residual Image - Jack Thorne

Jack Thorne Harvard University February 3, 2011 GALOIS REPRESENTATIONS AND AUTOMORPHIC FORMS SEMINAR For more videos, visit http://video.ias.edu

From playlist Mathematics

Video thumbnail

Important Math Proof: The Set of Equivalence Classes Partition a Set

In this video I prove a very important result in mathematics. Given an equivalence relation R on a nonempty set A, the set S of equivalence classes of A is a partition of A. Stated another way, this result says we can write A as a disjoint union of equivalence classes. The pencils I used

From playlist Relations

Video thumbnail

Linux Essentials For Hackers - #9 - Find + OverTheWire Bandit Challenge

Welcome to the Linux Essentials For Hackers series, where we will be covering the 20% you need to know to be efficient with Linux. In this video, we will be covering how to use the find command in Linux and we will be solving the OverTheWire Bandit wargame challenge. OverTheWire: https://

From playlist Linux Essentials For Hackers

Related pages

Pierre Samuel | Group (mathematics) | Néron–Severi group | Curve | Projective line | Intersection theory | Mathematics | Function (mathematics) | Standard conjectures on algebraic cycles | Algebraic geometry | Motive (algebraic geometry) | Category (mathematics) | Chow's moving lemma | Weil cohomology theory | Divisor (algebraic geometry) | Equivalence relation | Griffiths group | Correspondence (algebraic geometry) | Flat morphism | Graph of a function