Symmetric functions | Algebraic number theory
In mathematics, the Newton polygon is a tool for understanding the behaviour of polynomials over local fields, or more generally, over ultrametric fields. In the original case, the local field of interest was essentially the field of formal Laurent series in the indeterminate X, i.e. the field of fractions of the formal power series ring ,over , where was the real number or complex number field. This is still of considerable utility with respect to Puiseux expansions. The Newton polygon is an effective device for understanding the leading terms of the power series expansion solutions to equations where is a polynomial with coefficients in , the polynomial ring; that is, implicitly defined algebraic functions. The exponents here are certain rational numbers, depending on the chosen; and the solutions themselves are power series in with for a denominator corresponding to the branch. The Newton polygon gives an effective, algorithmic approach to calculating . After the introduction of the p-adic numbers, it was shown that the Newton polygon is just as useful in questions of ramification for local fields, and hence in algebraic number theory. Newton polygons have also been useful in the study of elliptic curves. (Wikipedia).
From playlist Physics - Newton's law videos for analysis
From playlist Physics - Newton's law videos for analysis
From playlist Physics - Newton's law videos for analysis
From playlist Physics - Newton's law videos for analysis
From playlist Physics - Newton's law videos for analysis
From playlist Physics - Newton's law videos for analysis
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From playlist Science Unplugged: Physics
From playlist Physics - Newton's law videos for analysis
Miaofen Chen - Newton stratification and weakly admissible locus in p-adic Hodge theory
Correction: The affiliation of Lei Fu is Tsinghua University. Rapoport and Zink introduce the p-adic period domain (also called the admissible locus) inside the rigid analytic p-adic flag varieties. The weakly admissible locus is an approximation of the admissible locus in the sense that
From playlist Conférence « Géométrie arithmétique en l’honneur de Luc Illusie » - 5 mai 2021
From playlist Physics - Newton's law videos for analysis
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
Newton above Hodge introduction part 2
This is a second video in the Newton above Hodge series.
From playlist Newton above Hodge
Christian Liedtke: Crystalline cohomology, period maps, and applications to K3 surfaces
Abstract: I will first introduce K3 surfaces and determine their algebraic deRham cohomology. Next, we will see that crystalline cohomology (no prior knowledge assumed) is the "right" replacement for singular cohomology in positive characteristic. Then, we will look at one particular class
From playlist Algebraic and Complex Geometry
Newton above Hodge Introduction part 3
Here we show where the hard parts of this theorem go to hide.
From playlist Newton above Hodge
Taylor Dupuy (Nov. 13, 2020): Abelian Varieties Over Finite Fields in the LMFDB
I will talk about things around the LMFDB database of isogeny classes of abelian varieties over finite fields (and maybe even about isomorphism classes). These could include: --"Sato-Ain't" distributions, --weird Tate classes, --Bizzaro Hodge co-levels (and very strange Ax-Katz/Cheval
From playlist Seminar Talks
Algebraic geometry 48: Newton's rotating ruler
This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It describes how to use Newton's rotating ruler to expand algebraic functions as power series. One application is that the field of complex Puiseux series is algebraicall
From playlist Algebraic geometry I: Varieties
From playlist Physics - Newton's law videos for analysis