In algebra, a commutative k-algebra A is said to be 0-smooth if it satisfies the following lifting property: given a k-algebra C, an ideal N of C whose square is zero and a k-algebra map , there exists a k-algebra map such that u is v followed by the canonical map. If there exists at most one such lifting v, then A is said to be 0-unramified (or 0-neat). A is said to be 0-étale if it is 0-smooth and 0-unramified. The notion of 0-smoothness is also called formal smoothness. A finitely generated k-algebra A is 0-smooth over k if and only if Spec A is a smooth scheme over k. A separable algebraic field extension L of k is 0-étale over k. The formal power series ring is 0-smooth only when and (i.e., k has a finite p-basis.) (Wikipedia).
Linear Algebra: Continuing with function properties of linear transformations, we recall the definition of an onto function and give a rule for onto linear transformations.
From playlist MathDoctorBob: Linear Algebra I: From Linear Equations to Eigenspaces | CosmoLearning.org Mathematics
Advanced Linear Algebra Full Video Course
Linear algebra is central to almost all areas of mathematics. For instance, #linearalgebra is fundamental in modern presentations of geometry, including for defining basic objects such as lines, planes and rotations. Also, functional analysis may be basically viewed as the application of
From playlist Linear Algebra
Prerequisites of a smooth function.
From playlist Advanced Calculus / Multivariable Calculus
Linear Algebra for Beginners | Linear algebra for machine learning
Linear algebra is the branch of mathematics concerning linear equations such as linear functions and their representations through matrices and vector spaces. Linear algebra is central to almost all areas of mathematics. In this course you will learn most of the basics of linear algebra wh
From playlist Linear Algebra
Using the general and vector forms of the equation of a plane from the normal and a point, or two points on the plane.
From playlist Linear Algebra
Algebra for Beginners | Basics of Algebra
#Algebra is one of the broad parts of mathematics, together with number theory, geometry and analysis. In its most general form, algebra is the study of mathematical symbols and the rules for manipulating these symbols; it is a unifying thread of almost all of mathematics. Table of Conten
From playlist Linear Algebra
10A An Introduction to Eigenvalues and Eigenvectors
A short description of eigenvalues and eigenvectors.
From playlist Linear Algebra
Linear Transformations: One-One
Linear Algebra: We recall the definition of one-one for functions and apply it to linear transformations. We obtain a simple rule for checking one-one in this case: either the kernel is zero or the associated matrix has a pivot in each column in row echelon form. Several examples are gi
From playlist MathDoctorBob: Linear Algebra I: From Linear Equations to Eigenspaces | CosmoLearning.org Mathematics
Akhil Mathew - Some recent advances in syntomic cohomology (3/3)
Bhatt-Morrow-Scholze have defined integral refinements $Z_p(i)$ of the syntomic cohomology of Fontaine-Messing and Kato. These objects arise as filtered Frobenius eigenspaces of absolute prismatic cohomology and should yield a theory of "p-adic étale motivic cohomology" -- for example, the
From playlist Franco-Asian Summer School on Arithmetic Geometry (CIRM)
Algebraic groups in positive characteristic - Srimathy Srinivasan
Short talks by postdoctoral members Topic: Algebraic groups in positive characteristic Speaker: Srimathy Srinivasan Affiliation: Member, School of Mathematics Date: October 4, 2017 For more videos, please visit http://video.ias.edu
From playlist Mathematics
Erik van Erp: Lie groupoids in index theory 1
The lecture was held within the framework of the Hausdorff Trimester Program Non-commutative Geometry and its Applications. 9.9.2014
From playlist HIM Lectures: Trimester Program "Non-commutative Geometry and its Applications"
Oliver Gabriel: Functorial Rieffel deformations and (periodic) cyclic cohomology
Inspired by previous work by S. Brain, G. Landi and W. van Suijlekom, we study functorial deformations of algebras and modules based on actions of Abelian locally compact groups. We consider the case of G = S^1 \times \mathbb Z, provide an explicit form for the deformation and show how fun
From playlist HIM Lectures: Trimester Program "Non-commutative Geometry and its Applications"
Hodge Theory -- From Abel to Deligne - Phillip Griffiths
Phillip Griffiths School of Mathematics, Institute for Advanced Study October 14, 2013 For more videos, visit http://video.ias.edu
From playlist Mathematics
Erik van Erp: Lie groupoids in index theory 2
The lecture was held within the framework of the Hausdorff Trimester Program Non-commutative Geometry and its Applications. 9.9.2014
From playlist HIM Lectures: Trimester Program "Non-commutative Geometry and its Applications"
Paolo Piazza: Proper actions of Lie groups and numeric invariants of Dirac operators
HYBRID EVENT shall explain how to define and investigate primary and secondary invariants of G-invariant Dirac operators on a cocompact G-proper manifold, with G a connected real reductive Lie group. This involves cyclic cohomology and Ktheory. After treating the case of cyclic cocycles a
From playlist Lie Theory and Generalizations
Olivier Benoist: Algebraic approximation of submanifolds of real algebraic varieties
CONFERENCE Recording during the thematic meeting : "Real Aspects of Geometry" the November 1, 2022 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIRM's Audi
From playlist Algebraic and Complex Geometry
Linear Algebra 2n: Spanning Sets
https://bit.ly/PavelPatreon https://lem.ma/LA - Linear Algebra on Lemma http://bit.ly/ITCYTNew - Dr. Grinfeld's Tensor Calculus textbook https://lem.ma/prep - Complete SAT Math Prep
From playlist Part 1 Linear Algebra: An In-Depth Introduction with a Focus on Applications
M. Pflaum: Localization in Hochschild homology and convolution algebras of circle actions
Talk by Shintaro Nishikawa in Global Noncommutative Geometry Seminar (Americas) http://www.math.wustl.edu/~xtang/NCG-Seminar.html on July 29, 2020.
From playlist Global Noncommutative Geometry Seminar (Americas)