Kazuya Kato - Logarithmic abelian varieties
Correction: The affiliation of Lei Fu is Tsinghua University. This is a joint work with T. Kajiwara and C. Nakayama. Logarithmic abelian varieties are degenerate abelian varieties which live in the world of log geometry of Fontaine-Illusie. They have group structures which do not exist in
From playlist Conférence « Géométrie arithmétique en l’honneur de Luc Illusie » - 5 mai 2021
This is one of my all-time favorite differential equation videos!!! :D Here I'm actually using the Wronskian to actually find a nontrivial solution to a second-order differential equation. This is amazing because it brings the concept of the Wronskian back to life! And as they say, you won
From playlist Differential equations
Jacob explains the fundamental concepts in group theory of what groups and subgroups are, and highlights a few examples of groups you may already know. Abelian groups are named in honor of Niels Henrik Abel (https://en.wikipedia.org/wiki/Niels_Henrik_Abel), who pioneered the subject of
From playlist Basics: Group Theory
We give a buttload of definitions for morphisms on various categories of complexes. The derived category of an abelian category is a category whose objects are cochain complexes and whose morphisms I describe in this video.
From playlist Derived Categories
Every Group of Order Five or Smaller is Abelian Proof
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Every Group of Order Five or Smaller is Abelian Proof. In this video we prove that if G is a group whose order is five or smaller, then G must be abelian.
From playlist Abstract Algebra
Abelian varieties not isogenous to Jacobians - Jacob Tsimerman
Joint IAS/Princeton University Number Theory Seminar Topic: Abelian varieties not isogenous to Jacobians Speaker: Jacob Tsimerman Affiliation: University of Toronto Date: December 01, 2021 Katz and Oort raised the following question: Given an algebraically closed field k, and a positive
From playlist Mathematics
David Masser: Avoiding Jacobians
Abstract: It is classical that, for example, there is a simple abelian variety of dimension 4 which is not the jacobian of any curve of genus 4, and it is not hard to see that there is one defined over the field of all algebraic numbers \overline{\bf Q}. In 2012 Chai and Oort asked if ther
From playlist Algebraic and Complex Geometry
Before we carry on with our coset journey, we need to discover when the left- and right cosets are equal to each other. The obvious situation is when our group is Abelian. The other situation is when the subgroup is a normal subgroup. In this video I show you what a normal subgroup is a
From playlist Abstract algebra
Stefano Marseglia, Computing isomorphism classes of abelian varieties over finite fields
VaNTAGe Seminar, February 1, 2022 License: CC-BY-NC-SA Links to some of the papers mentioned in this talk: Honda: https://doi.org/10.2969/jmsj/02010083 Tate: https://link.springer.com/article/10.1007/BF01404549 Deligne: https://eudml.org/doc/141987 Hofmann, Sircana: https://arxiv.org/ab
From playlist Curves and abelian varieties over finite fields
Group theory 17: Finite abelian groups
This lecture is part of a mathematics course on group theory. It shows that every finitely generated abelian group is a sum of cyclic groups. Correction: At 9:22 the generators should be g, h+ng not g, g+nh
From playlist Group theory
Ananth Shankar, Picard ranks of K3 surfaces and the Hecke orbit conjecture
VaNTAGe Seminar, November 23, 2021
From playlist Complex multiplication and reduction of curves and abelian varieties
Francesc Fité, Sato-Tate groups of abelian varieties of dimension up to 3
VaNTAGe seminar on April 7, 2020 License: CC-BY-NC-SA Closed captions provided by Jun Bo Lau.
From playlist The Sato-Tate conjecture for abelian varieties
Lucia Mocz: A new Northcott property for Faltings height
Abstract: The Faltings height is a useful invariant for addressing questions in arithmetic geometry. In his celebrated proof of the Mordell and Shafarevich conjectures, Faltings shows the Faltings height satisfies a certain Northcott property, which allows him to deduce his finiteness stat
From playlist Algebraic and Complex Geometry
What is the Mordell-Lang problem?
It is my intention to eventually explain some things about the Mordell-Lang problem and the higher dimensional versions of these. The presentation in this video is due to Mazur and can be found in an MSRI article he wrote that introduces these things.
From playlist Mordell-Lang
Christelle Vincent, Exploring angle rank using the LMFDB
VaNTAGe Seminar, February 15, 2022 License: CC-NC-BY-SA Links to some of the papers mentioned in the talk: Dupuy, Kedlaya, Roe, Vincent: https://arxiv.org/abs/2003.05380 Dupuy, Kedlaya, Zureick-Brown: https://arxiv.org/abs/2112.02455 Zarhin 1979: https://link.springer.com/article/10.100
From playlist Curves and abelian varieties over finite fields
Rachel Pries - The geometry of p-torsion stratifications of the moduli space of curve
The geometry of p-torsion stratifications of the moduli space of curve
From playlist 28ème Journées Arithmétiques 2013
Valentijn Karemaker, Mass formulae for supersingular abelian varieties
VaNTAGe seminar, Jan 18, 2022 License: CC-BY-NC-SA Links to some of the papers mentioned in this talk: Oort: https://link.springer.com/chapter/10.1007/978-3-0348-8303-0_13 Honda: https://doi.org/10.2969/jmsj/02010083 Tate: https://link.springer.com/article/10.1007/BF01404549 Tate: https
From playlist Curves and abelian varieties over finite fields
Claire Voisin: Gonality and zero-cycles of abelian varieties
Abstract: The gonality of a variety is defined as the minimal gonality of curve sitting in the variety. We prove that the gonality of a very general abelian variety of dimension g goes to infinity with g. We use for this a (straightforward) generalization of a method due to Pirola that we
From playlist Algebraic and Complex Geometry
