Mathematical terminology | Algebraic geometry | Algebraic number theory
In mathematics, the Frobenius endomorphism is defined in any commutative ring R that has characteristic p, where p is a prime number. Namely, the mapping φ that takes r in R to rp is a ring endomorphism of R. The image of φ is then Rp, the subring of R consisting of p-th powers. In some important cases, for example finite fields, φ is surjective. Otherwise φ is an endomorphism but not a ring automorphism. The terminology of geometric Frobenius arises by applying the spectrum of a ring construction to φ. This gives a mapping φ*: Spec(Rp) → Spec(R) of affine schemes. Even in cases where Rp = R this is not the identity, unless R is the prime field. Mappings created by fibre product with φ*, i.e. base changes, tend in scheme theory to be called geometric Frobenius. The reason for a careful terminology is that the Frobenius automorphism in Galois groups, or defined by transport of structure, is often the inverse mapping of the geometric Frobenius. As in the case of a cyclic group in which a generator is also the inverse of a generator, there are in many situations two possible definitions of Frobenius, and without a consistent convention some problem of a minus sign may appear. (Wikipedia).
C73 Introducing the theorem of Frobenius
The theorem of Frobenius allows us to calculate a solution around a regular singular point.
From playlist Differential Equations
The Frobenius Problem - Method for Finding the Frobenius Number of Two Numbers
Goes over how to find the Frobenius Number of two Numbers.
From playlist ℕumber Theory
The Frobenius Problem - Proof of the Formula for the Frobenius Number for Two Numbers
Describes how to derive the general formula for the Frobenius Number of two Numbers. Proves why Frob(m,n) = mn - m - n.
From playlist Proofs
Math 060 Linear Algebra 34 120814: Singular Value Decomposition and Low-rank Approximation (1/2)
Use of the Singular Value Decomposition: best low-rank approximation of a matrix. Frobenius norm not affected by orthogonal matrices; distance of a matrix to the space of matrices of rank k or lower; construction of a matrix that achieves that distance, using the SVD.
From playlist Course 4: Linear Algebra
Order of Arithmetic Operations: PEMDAS
Sometimes there are expressions that contain a number of different arithmetic operations. But how do we evaluate these? Left to right? Right to left? Does it matter? Someone make a decision! Well, someone did, and we have a strict algorithm that tells us the order in which we evaluate arit
From playlist Mathematics (All Of It)
Duco van Straten: CY-motives and differential equations
conference Recorded during the meeting "D-Modules: Applications to Algebraic Geometry, Arithmetic and Mirror Symmetry" the April 12, 2022 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by
From playlist Algebraic and Complex Geometry
Orthogonality and Orthonormality
We know that the word orthogonal is kind of like the word perpendicular. It implies that two vectors have an angle of ninety degrees or half pi radians between them. But this term means much more than this, as we can have orthogonal matrices, or entire subspaces that are orthogonal to one
From playlist Mathematics (All Of It)
Richard Taylor "Reciprocity Laws" [2012]
Slides for this talk: https://drive.google.com/file/d/1cIDu5G8CTaEctU5qAKTYlEOIHztL1uzB/view?usp=sharing Richard Taylor "Reciprocity Laws" Abstract: Reciprocity laws provide a rule to count the number of solutions to a fixed polynomial equation, or system of polynomial equations, modu
From playlist Number Theory
Sam Raskin - 1/2 What does geometric Langlands mean to a number theorist?
Sam Raskin (Univ. Texas)
From playlist 2022 Summer School on the Langlands program
Moduli spaces of local G-shtukas – Eva Viehmann – ICM2018
Lie Theory and Generalizations Invited Lecture 7.6 Moduli spaces of local G-shtukas Eva Viehmann Abstract: We give an overview of the theory of local G-shtukas and their moduli spaces that were introduced in joint work of U. Hartl and the author, and in the past years studied by many peo
From playlist Lie Theory and Generalizations
Geometry of Frobenioids - part 2 - (Set) Monoids
This is an introduction to the basic properties of Monoids. This video intended to be a starting place for log-schemes, Mochizuki's IUT or other absolute geometric constructions using monoids.
From playlist Geometry of Frobenioids
Cohomologies for rigid analytic varieties via motivic homotopy theory by Alberto Vezzani
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
Noémie Combe - How many Frobenius manifolds are there?
In this talk an overview of my recent results is presented. In a joint work with Yu. Manin (2020) we discovered that an object central to information geometry: statistical manifolds (related to exponential families) have an F-manifold structure. This algebraic structure is a more general v
From playlist Research Spotlight
Introduction to p-adic Hodge theory (Lecture 1) by Denis Benois
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) Eknat
From playlist Perfectoid Spaces 2019
Isocrystals associated to arithmetic jet spaces by Arnab Saha
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
Introduction to p-adic Hodge theory (Lecture 2) by Denis Benois
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
Geometry of Frobenioids - part 3 - What is a Frobenioid?
We will talk about the construction of Frobenioids in Mochizuki's Geometry of Frobenioids 1. Some nice links: https://plus.google.com/+lievenlebruyn/posts/Y1XVCDLWRP5https://plus.google.com/+lievenlebruyn/posts/Y1XVCDLWRP5 http://mathoverflow.net/questions/195353/what-is-a-frobenioid
From playlist Geometry of Frobenioids
11 - Représentations galoisiennes, motifs et fonctions L
Orateur(s) : J.-M. Fontaine Public : Tous Date : jeudi 27 octobre Lieu : Institut Henri Poincaré
From playlist Colloque Evariste Galois
The Frobenius conjecture in dimension two - Tony Yue Yu
Topic: The Frobenius conjecture in dimension two Speaker: Tony Yue Yu Affiliation: IAS Date: March 16, 2017 For more video, visit http://video.ias.edu
From playlist Mathematics