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ACCQ205 (courbes algébriques)
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notes-accq205.tex
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Reinterpretation of linear disjointness from extension of scalars.
David A. Madore
2016-03-18
1
-1
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+39
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Extension of scalars (of vector spaces and algebras) from a field to an ↵
David A. Madore
2016-03-18
1
-0
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+192
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extension field.
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Irreducibility versus geometric irreducibility.
David A. Madore
2016-03-18
1
-50
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+116
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Drawing of the three standard rational curves.
David A. Madore
2016-03-18
1
-7
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+53
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Examples of singular curves.
upload-20160317
David A. Madore
2016-03-17
1
-0
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+56
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Reducibility and irreducibility.
David A. Madore
2016-03-17
1
-0
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+53
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Note reducible curves.
David A. Madore
2016-03-17
1
-1
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+38
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Merge branch 'master' of git.madore.org:teach/accq205
David A. Madore
2016-03-17
1
-8
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+115
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Rational points, rational parametrization of the circle.
David A. Madore
2016-03-17
1
-8
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+115
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Two small additions/clarifications.
David A. Madore
2016-03-16
1
-3
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+9
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Definition of functions fields of curves.
David A. Madore
2016-03-16
1
-4
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+137
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Gauß lemma on irreducible polynomials.
David A. Madore
2016-03-16
1
-1
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+26
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Fix lots of typos (thanks, "Pjetri").
David A. Madore
2016-03-16
1
-14
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+14
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Some typos and other minor errors.
upload-20160307
David A. Madore
2016-03-07
1
-7
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+8
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Add disclaimer about provisional status of these notes.
upload-20160305
David A. Madore
2016-03-05
1
-0
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+7
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Add a few remarks.
David A. Madore
2016-03-05
1
-3
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+16
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Zariski-closed sets, radical ideals, and the bijection between them.
David A. Madore
2016-03-05
1
-6
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+212
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Note example of Artin's theorem on automorphisms.
David A. Madore
2016-03-05
1
-1
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+24
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Various hopefully intuitive explanations of Galois theory.
David A. Madore
2016-03-05
1
-0
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+78
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Two theorems by E. Artin.
David A. Madore
2016-03-05
1
-8
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+84
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State and prove the weak and strong Nullstellensätze.
David A. Madore
2016-03-03
1
-2
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+70
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Noetherian rings, maximal ideals of polynomial rings, and the Zariski lemma.
David A. Madore
2016-03-03
1
-17
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+191
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Typo.
David A. Madore
2016-03-03
1
-2
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+2
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Zeros-in-extension for algebraically closed fields.
David A. Madore
2016-03-02
1
-6
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+49
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Separating transcendence bases over a perfect field (not mentioning the term).
David A. Madore
2016-03-02
1
-18
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+65
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Typos.
David A. Madore
2016-03-02
1
-2
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+2
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Unfinished proof.
David A. Madore
2016-02-29
1
-1
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+24
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Statement of facts on Galois theory.
David A. Madore
2016-02-28
1
-6
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+165
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Mention purely inseparable extensions and the separable degree.
David A. Madore
2016-02-28
1
-1
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+30
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Split section on separable extensions.
David A. Madore
2016-02-28
1
-2
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+4
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A counterexample.
David A. Madore
2016-02-28
1
-0
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+16
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Separable algebraic extensions: compositum, etc.
David A. Madore
2016-02-28
1
-113
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+194
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Separable algebraic extensions.
David A. Madore
2016-02-27
1
-9
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+53
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Elements in a separably generated algebraic extension are separable.
David A. Madore
2016-02-27
1
-14
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+53
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More on linear disjointness.
David A. Madore
2016-02-27
1
-8
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+50
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More about separable algebraic elements.
David A. Madore
2016-02-27
1
-22
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+127
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Add trivial remark.
David A. Madore
2016-02-15
1
-0
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+3
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Nilradical of a ring.
David A. Madore
2016-02-15
1
-0
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+39
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An algebraic extension of a perfect field is perfect.
David A. Madore
2016-02-15
1
-2
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+28
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Minor updates.
David A. Madore
2016-02-15
1
-2
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+10
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TODO.
David A. Madore
2016-02-13
1
-0
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+6
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Separable element, perfect fields, primitive element theorem
David A. Madore
2016-02-13
1
-11
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+116
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Linear disjointness, subextensions of finite type.
David A. Madore
2016-02-12
1
-33
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+266
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Decomposition field for infinite families of polynomials.
David A. Madore
2016-02-12
1
-18
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+60
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Algebraic closure, Steinitz's theorem.
David A. Madore
2016-02-12
1
-1
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+43
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Rupture field, decomposition field, algebraic closure.
David A. Madore
2016-02-12
1
-7
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+109
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Additivity of transcendence degrees.
David A. Madore
2016-02-11
1
-6
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+44
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More about algebraic extensions. Transcendence degree.
David A. Madore
2016-02-10
1
-26
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+232
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Discuss generated algebra and field in general.
David A. Madore
2016-02-10
1
-95
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+214
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Recall what an integral domain is, and whatnot.
David A. Madore
2016-02-09
1
-13
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+79
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