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15
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When a holomorphy ring is a PID?

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#algebraic-geometry #commutative-algebra #finite-fields #principal-ideal-domains #function-fields
179
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Unramified Galois extension of a function field of a curve - definition

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#galois-theory #curves #function-fields #ramification
765
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Infinite places of a global function field

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#field-theory #algebraic-number-theory #function-fields
218
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Definition of a valuation on the points of an elliptic curves

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#algebraic-geometry #elliptic-curves #valuation-theory #function-fields
61
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Exact sequence of Riemann-Roch spaces and adeles

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#algebraic-geometry #field-theory #algebraic-number-theory #function-fields
89
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For every function field $F/K$ there exists $x\in F$ with $F/K(x)$ separable

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#field-theory #arithmetic-geometry #function-fields
36
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$\mathcal{O}_S$ holomorphy ring, $S$ containing almost all places $\Rightarrow O_S=K[x_1,...,x_r]$

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#commutative-algebra #arithmetic-geometry #function-fields
66
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Checking the Hasse-Weil bound for genus zero

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#algebraic-geometry #arithmetic-geometry #function-fields
110
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$f(t,x)$ irreducible, unsolvable over $\mathbb Q(t)$ such that its specialization $f(t_0,t)$ over $\mathbb Q$ is inseparable and (un)solvable.

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#polynomials #galois-theory #irreducible-polynomials #function-fields
181
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transcendental extension $\mathbb{C}(x)$ over $\mathbb{C}$, finding fixed field

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#abstract-algebra #field-theory #galois-theory #function-fields
43
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Imaginary quadratic extensions in characteristic 2

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#field-theory #finite-fields #local-field #function-fields
144
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Books for function fields and algebraic curves

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#algebraic-geometry #algebraic-number-theory #book-recommendation #function-fields
70
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What is the number/structure of units in a function field over $\mathbb{F}_q$?

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#abstract-algebra #number-theory #field-theory #function-fields
65
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Algebraic closure of completions in function fields

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#field-theory #local-field #function-fields
96
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Understanding the group of divisors of a function field and when two extensions of function fields isomorphic

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#number-theory #field-theory #extension-field #function-fields

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