In mathematics, a supersingular variety is (usually) a smooth projective variety in nonzero characteristic such that for all n the slopes of the Newton polygon of the nth crystalline cohomology are all n/2. For special classes of varieties such as elliptic curves it is common to use various ad hoc definitions of "supersingular", which are (usually) equivalent to the one given above. The term "singular elliptic curve" (or "singular j-invariant") was at one times used to refer to complex elliptic curves whose ring of endomorphisms has rank 2, the maximum possible. Helmut Hasse discovered that, in finite characteristic, elliptic curves can have larger rings of endomorphisms of rank 4, and these were called "supersingular elliptic curves". Supersingular elliptic curves can also be characterized by the slopes of their crystalline cohomology, and the term "supersingular" was later extended to other varieties whose cohomology has similar properties. The terms "supersingular" or "singular" do not mean that the variety has singularities. Examples include: * Supersingular elliptic curve. Elliptic curves in non-zero characteristic with an unusually large ring of endomorphisms of rank 4. * Supersingular Abelian variety Sometimes defined to be an abelian variety isogenous to a product of supersingular elliptic curves, and sometimes defined to be an abelian variety of some rank g whose endomorphism ring has rank (2g)2. * Supersingular K3 surface. Certain K3 surfaces in non-zero characteristic. * Supersingular Enriques surface. Certain Enriques surfaces in characteristic 2. * A surface is called Shioda supersingular if the rank of its Néron–Severi group is equal to its second Betti number. * A surface is called Artin supersingular if its formal Brauer group has infinite height. (Wikipedia).
#MegaFavNumbers What’s your Mega Favourite Number?
From playlist MegaFavNumbers
MegaFavNumbers :- Evenly Primest Prime 232,222,222,222,233,333,333,222,222,222,222,222,322,222,223
#MegaFavNumber
From playlist MegaFavNumbers
Noam Elkies, Supersingular reductions of elliptic curves
VaNTAGe seminar, October 26, 2021 License: CC-BY-NC-SA
From playlist Complex multiplication and reduction of curves and abelian varieties
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
Wanlin Li, A generalization of Elkies' theorem on infinitely many supersingular primes
VaNTAGe seminar, November 9, 2021 License: CC-BY-NC-SA
From playlist Complex multiplication and reduction of curves and abelian varieties
Factoring the GCF from a binomial, 4x^2 + 24x
👉Learn how to factor quadratics. A quadratic is an algebraic expression having two as the highest power of its variable(s). To factor an algebraic expression means to break it up into expressions that can be multiplied together to get the original expression. To factor a quadratic, all we
From playlist Factor Quadratic Expressions | GCF
There are a lot more numbers than I thought there were - MegaFavNumbers
A short video detailing my favorite number larger than 1 million! There are so many numbers out there it was hard to choose from, but I’m glad I could participate in the #MegaFavNumbers series
From playlist MegaFavNumbers
Summary for classifying polynomials
👉 Learn how to classify polynomials. A polynomial is an expression of the sums/differences of two or more terms having different interger exponents of the same variable. A polynomial can be classified in two ways: by the number of terms and by its degree. A monomial is an expression of 1
From playlist Classify Polynomials
Is it a monomial, binomial, trinomial, or polynomial
👉 Learn how to classify polynomials. A polynomial is an expression of the sums/differences of two or more terms having different interger exponents of the same variable. A polynomial can be classified in two ways: by the number of terms and by its degree. A monomial is an expression of 1
From playlist Classify Polynomials
Classifying a polynomial expression by subtraction
👉 Learn how to classify polynomials. A polynomial is an expression of the sums/differences of two or more terms having different interger exponents of the same variable. A polynomial can be classified in two ways: by the number of terms and by its degree. A monomial is an expression of 1
From playlist Classify Polynomials | Simplify First
Ben Howard: Supersingular points on som orthogonal and unitary Shimura varieties
To an orthogonal group of signature (n,2), or to a unitary group of any signature, one can attach a Shimura variety. The general problem is to describe the integral models of these Shimura varieties, and their reductions modulo various primes. I will give a conjectural description of the s
From playlist HIM Lectures: Junior Trimester Program "Algebraic Geometry"
Learn how to classify a polynomial based on the degree
👉 Learn how to classify polynomials. A polynomial is an expression of the sums/differences of two or more terms having different interger exponents of the same variable. A polynomial can be classified in two ways: by the number of terms and by its degree. A monomial is an expression of 1
From playlist Classify Polynomials
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
Factoring a binomial by distributive property
👉Learn how to factor quadratics. A quadratic is an algebraic expression having two as the highest power of its variable(s). To factor an algebraic expression means to break it up into expressions that can be multiplied together to get the original expression. To factor a quadratic, all we
From playlist Factor Quadratic Expressions | GCF
Benjamin Smith, Isogenies in genus 2 for cryptographic applications
VaNTAGe seminar, October 4, 2022 License: CC-BY-NC-SA
From playlist New developments in isogeny-based cryptography
Valentijn Karemaker - Mass formula for supersingular abelian threefolds - WAGON
Using the theory of polarised flag type quotients, we determine mass formulae for all principally polarised supersingular abelian threefolds defined over an algebraically closed field k of characteristic p. We combine these results with computations of the automorphism groups to study Oort
From playlist WAGON
Tomoyoshi Ibukiyama: Survey on quaternion hermitian lattices and its application to supersingular...
CIRM HYBRID EVENT The theme of the survey is how arithmetic theory of quatenion hermitian lattices can be applied to the theory of supersingular abelian varieties. Here the following geometric objects will be explained by arithmetics. Principal polarizations of superspecial abelian varieti
From playlist Number Theory
Chole Martindale, Torsion point attacks on the SIDH key exchange protocol
VaNTAGe Seminar, November 8, 2022 License: CC-BY-NC-SA Links to papers mentioned in the video: Jao-De Feo-Plut (2011): https://eprint.iacr.org/2011/506.pdf Galbraith-Petit-Shani-Ti (2016): https://eprint.iacr.org/2016/859 Petit (2017): https://eprint.iacr.org/2017/571 dQKLMPPS (2020): h
From playlist New developments in isogeny-based cryptography
👉 Learn how to classify polynomials. A polynomial is an expression of the sums/differences of two or more terms having different interger exponents of the same variable. A polynomial can be classified in two ways: by the number of terms and by its degree. A monomial is an expression of 1
From playlist Classify Polynomials
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