Morphisms of schemes

Locally acyclic morphism

In algebraic geometry, a morphism of schemes is said to be locally acyclic if, roughly, any sheaf on S and its restriction to X through f have the same étale cohomology, locally. For example, a smooth morphism is universally locally acyclic. (Wikipedia).

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Discrete-Time Dynamical Systems

This video shows how discrete-time dynamical systems may be induced from continuous-time systems. https://www.eigensteve.com/

From playlist Data-Driven Dynamical Systems

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ITHT: Part 9- The Homotopy Category

Credits: nLab: https://ncatlab.org/nlab/show/Introduction+to+Homotopy+Theory#TheHomotopyCategory Animation library: https://github.com/3b1b/manim​​​​​​​ My own code/modified library: https://github.com/treemcgee42/youtube​​​ Music: ► Artist Attribution • Music By: "KaizanBlu" • Track Nam

From playlist Introduction to Homotopy Theory

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Introduction to Homotopy Theory: Part 7- Small Object, Retract Arguments

Credits: nLab: https://ncatlab.org/nlab/show/Introdu...​ Animation library: https://github.com/3b1b/manim​​​​​ My own code/modified library: https://github.com/treemcgee42/youtube​ Music: ► Artist Attribution • Music By: "KaizanBlu" • Track Name: "Remember (Extended Mix)" • YouTube Track

From playlist Introduction to Homotopy Theory

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Model Categories by Rekha Santhanam

PROGRAM DUALITIES IN TOPOLOGY AND ALGEBRA (ONLINE) ORGANIZERS: Samik Basu (ISI Kolkata, India), Anita Naolekar (ISI Bangalore, India) and Rekha Santhanam (IIT Mumbai, India) DATE & TIME: 01 February 2021 to 13 February 2021 VENUE: Online Duality phenomena are ubiquitous in mathematics

From playlist Dualities in Topology and Algebra (Online)

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C07 Homogeneous linear differential equations with constant coefficients

An explanation of the method that will be used to solve for higher-order, linear, homogeneous ODE's with constant coefficients. Using the auxiliary equation and its roots.

From playlist Differential Equations

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Introduction to the z-Transform

http://AllSignalProcessing.com for more great signal processing content, including concept/screenshot files, quizzes, MATLAB and data files. Introduces the definition of the z-transform, the complex plane, and the relationship between the z-transform and the discrete-time Fourier transfor

From playlist The z-Transform

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ITHT: Part 10- Derived Functors

Credits: nLab: https://ncatlab.org/nlab/show/Introduction+to+Homotopy+Theory#DerivedFunctors Animation library: https://github.com/3b1b/manim​​​​​​​​ My own code/modified library: https://github.com/treemcgee42/youtub...​ Music: ► Artist Attribution • Music By: "KaizanBlu" • Track Name:

From playlist Introduction to Homotopy Theory

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Emily Riehl: On the ∞-topos semantics of homotopy type theory: The simplicial model of...- Lecture 2

HYBRID EVENT Recorded during the meeting "Logic and Interactions" the February 22, 2022 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual M

From playlist Topology

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Forced Harmonic Motion: Solution (5.6)

In this video, I find the particular solution to the equation of motion for a driven damped harmonic oscillator.

From playlist Intermediate Classical Mechanics

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Emily Riehl: On the ∞-topos semantics of homotopy type theory: All ∞-toposes have... - Lecture 3

HYBRID EVENT Recorded during the meeting "Logic and Interactions" the February 24, 2022 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual M

From playlist Topology

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Differential Equations: Complex Roots of the Characteristic Equation

Homogeneous, constant-coefficient differential equations have a characteristic or auxiliary equation. The solution(s) of this equation yield the particular solutions to the homogeneous differential equation which, when combined, produce a general solution. In this video, we explore the cas

From playlist Differential Equations

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Introduction to Homotopy Theory- Part 5- Transition to Abstract Homotopy Theory

Credits: nLab: https://ncatlab.org/nlab/show/Introdu...​ Animation library: https://github.com/3b1b/manim​​​ Music: ► Artist Attribution • Music By: "KaizanBlu" • Track Name: "Remember (Extended Mix)" • YouTube Track Link: https://bit.ly/31Ma5s0​​​ • Spotify Track Link: https://spoti.fi/

From playlist Introduction to Homotopy Theory

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Linear congruences

In this video we continue discussing congruences and, in particular, we discuss solutions of linear congruences. The content of this video corresponds to Section 4.4 of my book "Number Theory and Geometry" which you can find here: https://alozano.clas.uconn.edu/number-theory-and-geometry/

From playlist Number Theory and Geometry

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ITHT: Part 12- Model Structure on Topological Spaces

Credits: nLab: https://ncatlab.org/nlab/show/Introduction+to+Homotopy+Theory#TheClassicalModelStructureOfTopologicalSpaces Animation library: https://github.com/3b1b/manim​​​​​​​​​​ My own code/modified library: https://github.com/treemcgee42/youtub...

From playlist Introduction to Homotopy Theory

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Stable Homotopy Seminar, 4: Model categories (Ivo Vekemans)

This talk by Ivo Vekemans is a thorough introduction to model categories, presenting: weak factorization systems; the definition of model category and major examples (simplicial sets, topological spaces, and chain complexes); notions of homotopy in a model category, and the homotopy catego

From playlist Stable Homotopy Seminar

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Stable Homotopy Seminar, 8: The Stable Model Category of Spectra

We discuss the enrichment of spectra over spaces, and the compatibility of this enrichment with the model structure. Then we define the stable model structure by adding extra cofibrations to the levelwise model category of spectra, and restricting the weak equivalences to those maps which

From playlist Stable Homotopy Seminar

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Differential Equations: Distinct Roots of the Characteristic Equation

Homogeneous, constant-coefficient differential equations have a characteristic or auxiliary equation. The solution(s) of this equation yield the particular solutions to the homogeneous differential equation which, when combined, produce a general solution. In this video, we explore the mos

From playlist Differential Equations

Related pages

Smooth morphism | Scheme (mathematics) | Algebraic geometry | Étale cohomology | Sheaf (mathematics)