Theorems in algebraic geometry | Lemmas in algebra | Theorems in abstract algebra | Algebraic number theory
In mathematics, Abhyankar's lemma (named after Shreeram Shankar Abhyankar) allows one to kill tame ramification by taking an extension of a base field. More precisely, Abhyankar's lemma states that if A, B, C are local fields such that A and B are finite extensions of C, with ramification indices a and b, and B is tamely ramified over C and b divides a, then the compositumAB is an unramified extension of A. (Wikipedia).
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Yves André - Direct summand conjecture and perfectoid Abhyankar lemma: an overview
Séminaire Paris Pékin Tokyo / Mercredi 2 novembre 2016 According to Hochster's direct summand conjecture (1973), a regular ring R is a direct summand, as an R-module, of every finite extension ring. We shall outline our recent proof which relies on perfectoid techniques. Similar arguments
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Zero dimensional valuations on equicharacteristic (...) - B. Teissier - Workshop 2 - CEB T1 2018
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Frédéric Mangolte: Algebraic models of the line in the real affine plane
Abstract: We study the following real version of the famous Abhyankar-Moh Theorem: Which real rational map from the affine line to the affine plane, whose real part is a non-singular real closed embedding of ℝ into ℝ^2, is equivalent, up to a birational diffeomorphism of the plane, to the
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Regularity methods in combinatorics, number theory, and computer science - Jacob Fox
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9. Szemerédi's graph regularity lemma IV: induced removal lemma
MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019 Instructor: Yufei Zhao View the complete course: https://ocw.mit.edu/18-217F19 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP62qauV_CpT1zKaGG_Vj5igX Prof. Zhao explains a strengthening of the graph regulari
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6. Szemerédi's graph regularity lemma I: statement and proof
MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019 Instructor: Yufei Zhao View the complete course: https://ocw.mit.edu/18-217F19 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP62qauV_CpT1zKaGG_Vj5igX Szemerédi's graph regularity lemma is a powerful tool in
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Theory of numbers: Gauss's lemma
This lecture is part of an online undergraduate course on the theory of numbers. We describe Gauss's lemma which gives a useful criterion for whether a number n is a quadratic residue of a prime p. We work it out explicitly for n = -1, 2 and 3, and as an application prove some cases of Di
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A stable arithmetic regularity lemma in finite (...) - C. Terry - Workshop 1 - CEB T1 2018
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7. Szemerédi's graph regularity lemma II: triangle removal lemma
MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019 Instructor: Yufei Zhao View the complete course: https://ocw.mit.edu/18-217F19 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP62qauV_CpT1zKaGG_Vj5igX Continuing the discussion of Szemerédi's graph regularity
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László Lovász: The many facets of the Regularity Lemma
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