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15
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What is $[O_{L}:O]$ and $[O_{L}/(\pi):O/(\pi)]$?

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#modules #local-field #ramification
126
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Degree $n$ extension of local field splits degree $n$ division algebra

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#number-theory #local-field #division-algebras #brauer-group
165
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Adeles under base change

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#number-theory #class-field-theory #local-field
542
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Computing the degree of extension of local fields from the corresponding global fields

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#abstract-algebra #algebraic-number-theory #local-field
1k
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Why is every nonarchimedean local field of characteristic zero a finite extension of $\mathbb{Q}_p$?

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#field-theory #algebraic-number-theory #local-field
130
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Maximal Totally Ramified Extension

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#abstract-algebra #local-field #ramification
63
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Do all global fields have infinitely many principal prime ideals?

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#algebraic-number-theory #valuation-theory #local-field
41
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Restriction of a Generator of the Galois Group of the Compositum of Two Fields to the Subfields

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#field-theory #galois-theory #local-field
282
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Tate Cohomology of Squares

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#algebraic-number-theory #p-adic-number-theory #group-cohomology #local-field #galois-cohomology
482
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Valuations and different ideal in local fields

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#algebraic-number-theory #valuation-theory #local-field
50
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Different of an element references

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#reference-request #commutative-algebra #algebraic-number-theory #valuation-theory #local-field
56
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Absolute value of the difference is sufficiently small implies the quotient is close to 1

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#algebraic-number-theory #valuation-theory #local-field
60
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Why is $\mathbb{Q}_p\langle T\rangle/\mathfrak{m}$ a finite extension of $\mathbb{Q}_p$

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#number-theory #algebraic-number-theory #local-field
99
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Are there infinite extensions of $K$ inside $K^{ab}$ for $K$ local field?

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#abstract-algebra #field-theory #galois-theory #local-field
716
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Clarification about the definition of ring of integers of a local field

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#algebraic-number-theory #p-adic-number-theory #local-field #integer-rings

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