Commutative algebra 49: Completions
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 the completion of a ring and give some examples: the ring of formal power series, and the ring of 10-adic integers.
From playlist Commutative algebra
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
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
Rings and modules 1 Introduction
This lecture is part of an online course on ring theory, at about the level of a first year graduate course or honors undergraduate course. This is the introductory lecture, where we recall some basic definitions and examples, and describe the analogy between groups and rings. For the
From playlist Rings and modules
At 23:06 https://youtu.be/QgrvhjXyIIc?t=1386, I made a mistake, here is a more precise statement (also corrected later in the video): * the equality holds if degrees of A and B are different; * however, if deg A = deg B, then the sum may have a smaller degree, in the event that the leading
From playlist Abstract Algebra 2
Algebraic geometry 41: Completions
This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It reviews completions of rings and Hensel's lemma, and gives an example of two analytically isomorphic singularities.
From playlist Algebraic geometry I: Varieties
Abstract Algebra: The definition of a Ring
Learn the definition of a ring, one of the central objects in abstract algebra. We give several examples to illustrate this concept including matrices and polynomials. Be sure to subscribe so you don't miss new lessons from Socratica: http://bit.ly/1ixuu9W ♦♦♦♦♦♦♦♦♦♦ We recommend th
From playlist Abstract Algebra
Rings and modules 2: Group rings
This lecture is part of an online course on rings and modules. We decribe some examples of rings constructed from groups and monoids, such as group rings and rings of Dirichlet polynomials. For the other lectures in the course see https://www.youtube.com/playlist?list=PL8yHsr3EFj52XDLrm
From playlist Rings and modules
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
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
Commutative algebra 60: 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 define regular local rings as the local rings whose dimension is equal to the dimension of their cotangent space. We give s
From playlist Commutative algebra
Arthur-César Le Bras - Prismatic Dieudonné theory
Séminaire de Géométrie Arithmétique Paris-Pékin-Tokyo du 22 avril 2020 I would like to explain a classification result for p-divisible groups, which unifies many of the existing results in the literature. The main tool is the theory of prisms and prismatic cohomology recently developed by
From playlist Conférences Paris Pékin Tokyo
Kernel Recipes 2019 - Faster IO through io_uring
Since the dawn of time, Linux has had to make do with inferior IO interfaces. Native Linux AIO supports only a niche application class (O_DIRECT), and even for that use case, it’s far too slow for modern storage. This talk will detail io_uring, a modern IO interface for Linux, that’s both
From playlist Kernel Recipes 2019
Kęstutis Česnavičius - Purity for Flat Cohomology
The absolute cohomological purity conjecture of Grothendieck proved by Gabber ensures that on regular schemes étale cohomology classes of fixed cohomological degree extend uniquely over closed subschemes of large codimension. I will discuss the corresponding phenomenon for flat cohomology.
From playlist Journée Gretchen & Barry Mazur
Purity for flat cohomology by Kestutis Cesnavicius
PERFECTOID SPACES ORGANIZERS: Debargha Banerjee, Denis Benois, Chitrabhanu Chaudhuri, and Narasimha Kumar Cheraku DATE & TIME: 09 September 2019 to 20 September 2019 VENUE: Madhava Lecture Hall, ICTS, Bangalore Scientific committee: Jacques Tilouine (University of Paris, France) Eknath
From playlist Perfectoid Spaces 2019
Digression: THH of the integers (corrected)
In this video, we explain how to compute THH of the integers. In order to do this we compute it first relative to the element p and then use a spectral sequence to deduce the final result. This is a corrected version of the old video, in which I got the Hasse-squares at 13:10 and 24:20 w
From playlist Topological Cyclic Homology
This lecture is part of an online course on rings and modules. We continue the previous lecture on complete rings by discussing Hensel's lemma for finding roots of polynomials over p-adic rings or over power series rings. We sketch two proofs, by slowly improving a root one digit at a tim
From playlist Rings and modules