Algebraic geometry

Noetherian scheme

In algebraic geometry, a noetherian scheme is a scheme that admits a finite covering by open affine subsets , noetherian rings. More generally, a scheme is locally noetherian if it is covered by spectra of noetherian rings. Thus, a scheme is noetherian if and only if it is locally noetherian and quasi-compact. As with noetherian rings, the concept is named after Emmy Noether. It can be shown that, in a locally noetherian scheme, if is an open affine subset, then A is a noetherian ring. In particular, is a noetherian scheme if and only if A is a noetherian ring. Let X be a locally noetherian scheme. Then the local rings are noetherian rings. A noetherian scheme is a noetherian topological space. But the converse is false in general; consider, for example, the spectrum of a non-noetherian valuation ring. The definitions extend to formal schemes. (Wikipedia).

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Schemes 15: Quasicompact, Noetherian

This lecture is part of an online algebraic geometry course on schemes, based on chapter II of "Algebraic geometry" by Hartshorne. We define quasi-compact, Noetherian, and locally Noetherian schemes, give a few examples, and show that "locally Noetherian" is a local property.

From playlist Algebraic geometry II: Schemes

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Rings 17 Noetherian rings

This lecture is part of an online course on rings and modules. We define Noetherian rings, give several equivalent properties, and give some examples of rings that are or are not Noetherian. This will be continued in the next lecture about Hilbert's finiteness theorems. For the other

From playlist Rings and modules

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Commutative algebra 5 (Noetherian rings)

This lecture is part of an online course on commutative algebra, following the book "Commutative algebra with a view toward algebraic geometry" by David Eisenbud. In this lecture we find three equivalent ways of defining Noetherian rings, and give several examples of Noetherian and non-No

From playlist Commutative algebra

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algebraic geometry 6 Noetherian spaces

This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It covers Noetherian rings, Noetherian spaces, and irreducible sets.

From playlist Algebraic geometry I: Varieties

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Noetherianity up to Symmetry - Jan Draisma

Members' Colloquium Topic: Noetherianity up to Symmetry Speaker: Jan Draisma Affiliation: Member, School of Mathematics Date: October 17, 2022 Noetherianity is a fundamental property of modules, rings, and topological spaces that underlies much of commutative algebra and algebraic geomet

From playlist Mathematics

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The most beautiful idea in physics - Noether's Theorem

Homework: -What do you think of this idea? Have you heard of it before? -Maybe you’ve heard about things like super symmetry in physics- try find out how that’s related. -If you know some calculus and classical physics, try and find a proof of this theorem. -Try come up with strange sys

From playlist Some Quantum Mechanics

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Noether's works in Topology by Indranil Biswas

DATES: Monday 29 Aug, 2016 - Tuesday 30 Aug, 2016 VENUE: Madhava Lecture Hall, ICTS Bangalore Emmy Noether (1882­-1935) is well known for her famous contributions to abstract algebra and theoretical physics. Noether’s mathematical work has been divided into three ”epochs”. In the first (

From playlist The Legacy of Emmy Noether

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10/13/17 Yuri Berest

Differential Isomorphism and Equivalence of Algebraic Varieties Board at 49:35 Sum_i=1^N 2/(x-phi_i(y,t))^2

From playlist Fall 2017

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Ofer Gabber - Spreading-out of rigid-analytic families and observations on p-adic Hodge theory

(Joint work with Brian Conrad.) Let K be a complete rank 1 valued field with ring of integers OK, A an adic noetherian ring and f: A→OK an adic morphism. If g: X→Y is a proper flat morphism between rigid analytic spaces over Kthen locally on Y a flat formal model of gspreads out to a prope

From playlist Conférences Paris Pékin Tokyo

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Commutative algebra 15 (Noetherian spaces)

This lecture is part of an online course on commutative algebra, following the book "Commutative algebra with a view toward algebraic geometry" by David Eisenbud. In this lecture we define Noetherian topological spaces, and use them to show that for a Noetherian ring R, every closed subse

From playlist Commutative algebra

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Interplay of symmetries and other integrability quantifiers in finite by Lakhsmanan Muthusamy

DATES: Monday 29 Aug, 2016 - Tuesday 30 Aug, 2016 VENUE: Madhava Lecture Hall, ICTS Bangalore Emmy Noether (1882­-1935) is well known for her famous contributions to abstract algebra and theoretical physics. Noether’s mathematical work has been divided into three ”epochs”. In the first (

From playlist The Legacy of Emmy Noether

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Origin and Development of Valuation Theory by Sudesh Khanduja

DATES: Monday 29 Aug, 2016 - Tuesday 30 Aug, 2016 VENUE: Madhava Lecture Hall, ICTS Bangalore Emmy Noether (1882­-1935) is well known for her famous contributions to abstract algebra and theoretical physics. Noether’s mathematical work has been divided into three ”epochs”. In the first (

From playlist The Legacy of Emmy Noether

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Emmy Noether in Erlangen and Göttingen by Ravi Rao

DATES: Monday 29 Aug, 2016 - Tuesday 30 Aug, 2016 VENUE: Madhava Lecture Hall, ICTS Bangalore Emmy Noether (1882­-1935) is well known for her famous contributions to abstract algebra and theoretical physics. Noether’s mathematical work has been divided into three ”epochs”. In the first (

From playlist The Legacy of Emmy Noether

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Purity for the Brauer group of singular schemes - Česnavičius - Workshop 2 - CEB T2 2019

Kęstutis Česnavičius (Université Paris-Sud) / 27.06.2019 Purity for the Brauer group of singular schemes For regular Noetherian schemes, the cohomological Brauer group is insensitive to removing a closed subscheme of codimension ≥ 2. I will discuss the corresponding statement for scheme

From playlist 2019 - T2 - Reinventing rational points

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