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Results tagged with algebraic-number-theory
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user 105386
Algebraic number fields, Algebraic integers, Arithmetic Geometry, Elliptic Curves, Function fields, Local fields, Arithmetic groups, Automorphic forms, zeta functions, $L$-functions, Quadratic forms, Quaternion algebras, Homogenous forms, Class groups, Units, Galois theory, Group cohomology, Étale cohomology, Motives, Class field theory, Iwasawa theory, Modular curves, Shimura varieties, Jacobian varieties, Moduli spaces
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Definition of a Lubin Tate group
Let $L$ be a $p$-adic number field, $\mathcal{O}_L$ its ring of integers, $\pi$ a uniformizer of $L$ and $q$ the cardinality of its residue field.
Let $\varphi(t)\in \mathcal{O}_L[[t]]$ be a Frobeniu …
- 87
7
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Absolute value on tensor product of fields
Suppose that we have the Laurent series fields $F_1:=\mathbb F_p((X))$ and $F_2:=\mathbb F_p((Y))$.
Equip $F_1$ with the $X$-adic multiplicative absolute value $|\cdot|_1$, i.e. define $|X|_1=\dfrac{1 …
- 87
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2
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Norm on tensor product of fields
Let $F$ be an algebraically closed field of characteristic $p$ equipped with an absolute value $|\cdot|:F \rightarrow \mathbb{R}_{\ge 0}$ with respect to which $F$ is complete.
Define $|\cdot|_{prod} …
- 87
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Quasi-algebraically closed fields reference request
I am looking for a road to understanding what quasi-algebraically closed fields are with the ultimate goal of understanding the paper by Lang 1952.
My current background is the first 6 chapters from …
- 87
1
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1
answer
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Product absolute value in rings of integers
Let $F$ be an algebraically closed field of characteristic $p$ equipped with a nonarchimedean dense absolute value $|\cdot|:F \rightarrow \mathbb{R}_{\ge 0}$ with respect to which $F$ is complete. Let …
- 87