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100
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When does a number field have $p$-rank greater than $n$?

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#number-theory #algebraic-number-theory #class-field-theory #galois-cohomology
364
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Is $\mu_n$ a locally constant sheaf for the Zariski topology?

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#algebraic-geometry #algebraic-number-theory #sheaf-theory
37
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Property of quotient ideals in a number Field

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#linear-algebra #ring-theory #field-theory #algebraic-number-theory #ideals
106
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Inclusion of quotient ideals. if $I \subseteq J$, then $I/qI \subseteq J/qJ$?

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#ring-theory #field-theory #algebraic-number-theory #ideals
115
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What does it mean to say a quotient of fractional ideals?

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#abstract-algebra #ring-theory #algebraic-number-theory #ideals
390
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An algebraic proof that every finite extension of $\mathbb Q$ is ramified?

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#algebraic-geometry #commutative-algebra #algebraic-number-theory
983
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Express the inertia group in terms of the maximal unramified extension

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#abstract-algebra #notation #galois-theory #algebraic-number-theory #extension-field
978
Views

Calculating class numbers

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#algebraic-number-theory #ideals #principal-ideal-domains #cyclotomic-fields #ideal-class-group
90
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Can a primitive integral polynomial represent integers prime to any number?

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#abstract-algebra #elementary-number-theory #polynomials #algebraic-number-theory
128
Views

Show that $\langle\,23 \rangle\ =\langle\, 23 , \alpha-10\rangle^2 \langle\, 23, \alpha-3 \rangle$

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#number-theory #algebraic-number-theory
51
Views

Can we finitely extend a field with Galois group $S_n$ to a a field with a given permutation group

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#galois-theory #algebraic-number-theory #symmetric-groups
81
Views

$\langle 3 \rangle$ in $\textbf{Z}[\omega]$ ramifies, not splits, right?

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#algebraic-number-theory
191
Views

How to distinguish algebraic numbers as roots?

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#algebraic-number-theory
106
Views

Isomorphism of Weil representations only when $E/F$ is Galois?

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#number-theory #representation-theory #algebraic-number-theory #langlands-program
138
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Non-Galois finite extensions of $F^{\operatorname{ur}}$

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#galois-theory #algebraic-number-theory #p-adic-number-theory #class-field-theory #local-field

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