Commutative algebra | Algebraic geometry
In algebraic geometry, a geometrically regular ring is a Noetherian ring over a field that remains a regular ring after any finite extension of the base field. Geometrically regular schemes are defined in a similar way. In older terminology, points with regular local rings were called simple points, and points with geometrically regular local rings were called absolutely simple points. Over fields that are of characteristic 0, or algebraically closed, or more generally perfect, geometrically regular rings are the same as regular rings. Geometric regularity originated when Claude Chevalley and André Weil pointed out to Oscar Zariski that, over non-perfect fields, the for a simple point of an algebraic variety is not equivalent to the condition that the local ring is regular. A Noetherian local ring containing a field k is geometrically regular over k if and only if it is formally smooth over k. (Wikipedia).
Definition of a Ring and Examples of Rings
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Definition of a Ring and Examples of Rings - Definition of a Ring. - Definition of a commutative ring and a ring with identity. - Examples of Rings include: Z, Q, R, C under regular addition and multiplication The Ring of all n x
From playlist Abstract Algebra
Geometric Algebra - Rotors and Quaternions
In this video, we will take note of the even subalgebra of G(3), see that it is isomorphic to the quaternions and, in particular, the set of rotors, themselves in the even subalgebra, correspond to the set of unit quaternions. This brings the entire subject of quaternions under the heading
From playlist Math
Ring Theory: We define rings and give many examples. Items under consideration include commutativity and multiplicative inverses. Example include modular integers, square matrices, polynomial rings, quaternions, and adjoins of algebraic and transcendental numbers.
From playlist Abstract Algebra
Geometry: Ch 4 - Geometric Figures (8 of 18) The Regular Pentagon
Visit http://ilectureonline.com for more math and science lectures! In this video I will find the 3 angles of the regular pentagon and its parameter and area. Next video in this series can be seen at: https://youtu.be/3G_jjW1d280
From playlist GEOMETRY 4 - GEOMETRIC FIGURES
Units in a Ring (Abstract Algebra)
The units in a ring are those elements which have an inverse under multiplication. They form a group, and this “group of units” is very important in algebraic number theory. Using units you can also define the idea of an “associate” which lets you generalize the fundamental theorem of ar
From playlist Abstract Algebra
Visual Group Theory, Lecture 7.1: Basic ring theory
Visual Group Theory, Lecture 7.1: Basic ring theory A ring is an abelian group (R,+) with a second binary operation, multiplication and the distributive law. Multiplication need not commute, nor need there be multiplicative inverses, so a ring is like a field but without these properties.
From playlist Visual Group Theory
Commutative algebra 61: Examples of regular local rings
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 give some examples of regular local rings. We first give an example of a regular local ring that is not geometrically regul
From playlist Commutative algebra
Kęstutis Česnavičius - Grothendieck–Serre in the quasi-split unramified case
Correction: The affiliation of Lei Fu is Tsinghua University. The Grothendieck–Serre conjecture predicts that every generically trivial torsor under a reductive group scheme G over a regular local ring R is trivial. We settle it in the case when G is quasi-split and R is unramified. To ov
From playlist Conférence « Géométrie arithmétique en l’honneur de Luc Illusie » - 5 mai 2021
Vincent LAFFORGUE - Stacks of Shtukas and spectral decompositions
https://ams-ems-smf2022.inviteo.fr/
From playlist International Meeting 2022 AMS-EMS-SMF
Abstract Algebra | What is a ring?
We give the definition of a ring and present some examples. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Abstract Algebra
Commutative algebra 66: Local complete intersection rings
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 define local complete intersection rings as regular local rings divided by a regular sequence. We give a few examples to il
From playlist Commutative algebra
Fourier transform for Class D-modules - David Ben Zvi
Locally Symmetric Spaces Seminar Topic: Fourier transform for Class D-modules Speaker: David Ben Zvi Affiliation: University of Texas at Austin; Member, School of Mathematics Date: Febuary 13, 2018 For more videos, please visit http://video.ias.edu
From playlist Mathematics
Affine Springer Fiber and Representation Theory of W algebra by Dan Xie
PROGRAM : QUANTUM FIELDS, GEOMETRY AND REPRESENTATION THEORY 2021 (ONLINE) ORGANIZERS : Aswin Balasubramanian (Rutgers University, USA), Indranil Biswas (TIFR, india), Jacques Distler (The University of Texas at Austin, USA), Chris Elliott (University of Massachusetts, USA) and Pranav Pan
From playlist Quantum Fields, Geometry and Representation Theory 2021 (ONLINE)
(Equivariant) Cohomology of the affine Grassmannian and Ginzburg’s picture - Linyuan Liu
Seminar on Geometric and Modular Representation Theory Topic: (Equivariant) Cohomology of the affine Grassmannian and Ginzburg’s picture Speaker: Linyuan Liu Affiliation: University of Sydney; Member, School of Mathematics Date: October 21, 2020 For more video please visit http://video.i
From playlist Mathematics
Emanuele Dotto: Real topological Hochschild homology and the Hermitian K-theory...
Emanuele Dotto: Real topological Hochschild homology and the Hermitian K theory of Z2 equivariant rin The lecture was held within the framework of the Hausdorff Trimester Program: K-Theory and Related Fields. Real topological Hochschild homology (THR) is a Z/2-equivariant spectrum introd
From playlist HIM Lectures: Trimester Program "K-Theory and Related Fields"
This lecture gives an introductory overview of the Chow ring of a nonsingular variety. The idea is to define a ring structure related to subvarieties with the product corresponding to intersection. There are several complications that have to be solved, in particular how to define intersec
From playlist Algebraic geometry: extra topics
Residual Intersections in Geometry and Algebra by David Eisenbud
DISTINGUISHED LECTURES RESIDUAL INTERSECTIONS IN GEOMETRY AND ALGEBRA SPEAKER: David Eisenbud (Director, Mathematical Sciences Research Institute, and Professor of Mathematics, UC Berkeley) DATE: 13 December 2019, 16:00 to 17:00 VENUE: Madhava Lecture Hall, ICTS-TIFR, Bengaluru In thi
From playlist DISTINGUISHED LECTURES
Abstract Algebra | The characteristic of a ring.
We define the characteristic of a ring and give some definitions. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Abstract Algebra
Herwig Hauser : Commutative algebra for Artin approximation - Part 3
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 Jean-Morlet Chair - Hauser/Rond