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definition of the L-function $L(f, \chi, s): \mathbb{A}_K \rightarrow \mathbb{C}$, what is smoothness and what is $f$?

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#number-theory #analytic-number-theory #class-field-theory #l-functions #adeles
330
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Unramified cubic extension of imaginary quadratic fields

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#algebraic-number-theory #class-field-theory
4.4k
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The maximal unramified extension of a local field may not be complete

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#field-theory #algebraic-number-theory #p-adic-number-theory #class-field-theory
138
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Existence of Conductor for Cyclotomic Extension (pg 200, Serge Lang A.N.T.)

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#number-theory #algebraic-number-theory #class-field-theory
315
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Finite dimensional central division algebras over a finite extension of $\mathbb{F}_q(T)$

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#noncommutative-algebra #class-field-theory #division-algebras
928
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What does it mean for a prime ideal to divide a natural number m?

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#class-field-theory #maximal-and-prime-ideals
1.2k
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Definition of Artin map

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#abstract-algebra #algebraic-number-theory #class-field-theory
598
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prime ideal of $\mathcal O_K$ splits completely in tower of Galois extensions

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#abstract-algebra #algebraic-number-theory #galois-theory #class-field-theory
532
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norm map and local class field theory

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#number-theory #algebraic-number-theory #class-field-theory
974
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How does class field theory help us deduce the splitting of nonprincipal prime ideals?

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#number-theory #algebraic-number-theory #class-field-theory
148
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How does $ \text{Gal}(K / k) $ act on ideles?

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#number-theory #algebraic-number-theory #class-field-theory
801
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Why is $Gal(\Omega/k)$ a topological group under the Krull topology?

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#general-topology #number-theory #galois-theory #topological-groups #class-field-theory
973
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Artin reciprocity theorem for Hilbert class field

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#algebraic-number-theory #class-field-theory
147
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$CL(O_S) \cong \mathbb{Z}/3\mathbb{Z}$.

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#abstract-algebra #number-theory #elementary-number-theory #algebraic-number-theory #class-field-theory
84
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Reference request: Cohomology of Elliptic Curves

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#algebraic-geometry #reference-request #galois-theory #class-field-theory

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