Duality theories | Galois theory | Theorems in algebraic number theory

Local Tate duality

In Galois cohomology, local Tate duality (or simply local duality) is a duality for Galois modules for the absolute Galois group of a non-archimedean local field. It is named after John Tate who first proved it. It shows that the dual of such a Galois module is the Tate twist of usual linear dual. This new dual is called the (local) Tate dual. Local duality combined with Tate's local Euler characteristic formula provide a versatile set of tools for computing the Galois cohomology of local fields. (Wikipedia).

Video thumbnail

Duality in Higher Categories-I by Pranav Pandit

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)

Video thumbnail

Duality Argument

In this video, I present a very classical example of a duality argument: Namely, I show that T^T is one-to-one if and only if T is onto and use that to show that T is one-to-one if and only if T^T is onto. This illustrates the beautiful interplay between a vector space and its dual space,

From playlist Dual Spaces

Video thumbnail

Thick And Localising Subcategories Of Derived Categories (Lecture-2) by Srikanth Iyengar

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)

Video thumbnail

Selmer groups and a Cassels-Tate pairing for finite Galois modules - Alexander Smith

Joint IAS/Princeton University Number Theory Seminar Topic: Selmer groups and a Cassels-Tate pairing for finite Galois modules Speraker: Alexander Smith Affiliation: Massachusetts Institute of Technology Date: February 25, 2021 For more video please visit http://video.ias.edu

From playlist Mathematics

Video thumbnail

Cyril Demarche: Cohomological obstructions to local-global principles - lecture 3

Hasse proved that for quadrics the existence of rational points reduces to the existence of solutions over local fields. In many cases, cohomological constructions provide obstructions to such a local to global principle. The objective of these lectures is to give an introduction to these

From playlist Algebraic and Complex Geometry

Video thumbnail

Every basis is a dual basis

In this video, I show a very neat result about dual spaces: Namely, any basis of V* is automatically a dual basis of some basis of V. Even though this result is very interesting, it's the proof that makes this very exciting, by simply using the fact that V and V** are 'very' isomorphic. En

From playlist Dual Spaces

Video thumbnail

Moduli of p-divisible groups (Lecture 4) by Ehud De Shalit

PROGRAM 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

From playlist Perfectoid Spaces 2019

Video thumbnail

Complexes of tori and rational points on homogeneous (...) - Harari - Workshop 1 - CEB T2 2019

David Harari (Université Paris Sud) / 20.05.2019 Complexes of tori and rational points on homogeneous spaces over a function field We explain new arithmetic duality theorems for finite group schemes and 2-term complexes of tori defined over a global field of positive characteristic. We

From playlist 2019 - T2 - Reinventing rational points

Video thumbnail

Jeremy Hahn : Prismatic and syntomic cohomology of ring spectra

CONFERENCE Recording during the thematic meeting : « Chromatic Homotopy, K-Theory and Functors» the January 24, 2023 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Jean Petit Find this video and other talks given by worldwide mathematicians on CIR

From playlist Topology

Video thumbnail

Moduli of p-divisible groups (Lecture 1) by Ehud De Shalit

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

Video thumbnail

Higher Algebra 12: The Tate construction

In this video we introduce the Tate construction and especially Tate spectra. This is defined as the cofibre of a certain norm map, which we introduced for completely general group objects and stable infinity categories. We then also explain what it has to do with Poncaré duality and that

From playlist Higher Algebra

Video thumbnail

Duality in Algebraic Geometry by Suresh Nayak

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)

Video thumbnail

Localization of Spaces by Somnath Basu

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)

Video thumbnail

Serre Duality on Character Varieties and Explicit Reciprocity Laws by Otmar Venjakob

PROGRAM ELLIPTIC CURVES AND THE SPECIAL VALUES OF L-FUNCTIONS (HYBRID) ORGANIZERS: Ashay Burungale (CalTech/UT Austin, USA), Haruzo Hida (UCLA), Somnath Jha (IIT Kanpur) and Ye Tian (MCM, CAS) DATE: 08 August 2022 to 19 August 2022 VENUE: Ramanujan Lecture Hall and online The program pla

From playlist ELLIPTIC CURVES AND THE SPECIAL VALUES OF L-FUNCTIONS (2022)

Video thumbnail

Introduction to Similarity

This video introduces similarity and explains how to determine if two figures are similar or not. http://mathispower4u.com

From playlist Number Sense - Decimals, Percents, and Ratios

Video thumbnail

Duality In Higher Categories III by Pranav Pandit

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)

Video thumbnail

Determining if two angles are adjacent or not

👉 Learn how to define and classify different angles based on their characteristics and relationships are given a diagram. The different types of angles that we will discuss will be acute, obtuse, right, adjacent, vertical, supplementary, complementary, and linear pair. The relationships

From playlist Angle Relationships From a Figure

Video thumbnail

Yonatan Harpaz - New perspectives in hermitian K-theory III

For questions and discussions of the lecture please go to our discussion forum: https://www.uni-muenster.de/TopologyQA/index.php?qa=k%26l-conference This lecture is part of the event "New perspectives on K- and L-theory", 21-25 September 2020, hosted by Mathematics Münster: https://go.wwu

From playlist New perspectives on K- and L-theory

Video thumbnail

Gonçalo Tabuada - 3/3 Noncommutative Counterparts of Celebrated Conjectures

Some celebrated conjectures of Beilinson, Grothendieck, Kimura, Tate, Voevodsky, Weil, and others, play a key central role in algebraic geometry. Notwithstanding the effort of several generations of mathematicians, the proof of (the majority of) these conjectures remains illusive. The aim

From playlist Summer School 2020: Motivic, Equivariant and Non-commutative Homotopy Theory

Video thumbnail

Identifying congruent parts between two polygons

👉 Learn how to solve with similar polygons. Two polygons are said to be similar if the corresponding angles are congruent (equal). When two polygons are similar the corresponding sides are proportional. Knowledge of the length of the sides or the proportion of the side lengths of one of th

From playlist Congruent Polygons

Related pages

Group representation | Vector space | Group cohomology | Tate twist | Duality (mathematics) | Local Euler characteristic formula | Cyclotomic character | Linear map | Cup product | Galois cohomology | Cohomological dimension | John Tate (mathematician) | Characteristic (algebra) | Global field | Tate duality | Tate module | Galois module | Absolute Galois group | Prime number | P-adic number