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Elliptic curve theory : Injection from $\widehat{E(K)}$ to $E(K_v)$

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#number-theory #algebraic-geometry #elliptic-curves #arithmetic-geometry #local-field
35
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Fix points of Galois action on etale homology

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#algebraic-geometry #arithmetic-geometry #etale-cohomology #poincare-duality
74
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Ramification of mod $\ell$ representation of elliptic curves

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#elliptic-curves #arithmetic-geometry #galois-representations
68
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Profinite completion of local Mordell-Weil group

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#number-theory #elliptic-curves #arithmetic-geometry
35
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rational elliptic curve: torsion subgroup defined over abelian extensions

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#arithmetic #elliptic-curves #arithmetic-geometry #cyclotomic-fields
22
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Local Tate pairing on elliptic curves

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#elliptic-curves #duality-theorems #arithmetic-geometry
114
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Notion of functions on Elliptic curves over scheme and writing them as power series.

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#number-theory #algebraic-geometry #algebraic-number-theory #elliptic-curves #arithmetic-geometry
23
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Mordell-Weil theorem for rational points on $y^2=x^2+1$

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#rational-numbers #arithmetic-geometry #finitely-generated
44
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Isomorphism $(A\times B)^\vee\to A^\vee\times B^\vee$ for abelian varieties

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#number-theory #algebraic-geometry #arithmetic-geometry #abelian-varieties #isogeny
32
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Application of the seesaw principle

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#arithmetic-geometry #abelian-varieties #line-bundles
53
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$\text{Im}(f)=\text{ker}(\widehat{f})$, written in 'Galois cohomology of elliptic curves' by Coates and Sujata

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#abstract-algebra #elliptic-curves #duality-theorems #arithmetic-geometry
40
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Pair of torsors and divisors and Galois cohomology

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#algebraic-geometry #elliptic-curves #arithmetic-geometry #divisors-algebraic-geometry #galois-cohomology
62
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Using étale fundamental group to show unramifiedness of Tate module

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#elliptic-curves #fundamental-groups #algebraic-groups #arithmetic-geometry #etale-cohomology
73
Views

Does $\text{Aut}(E)\cong E$ hołd for elliptic curves?

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#algebraic-geometry #elliptic-curves #arithmetic-geometry
22
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horizontal divisor and normalization

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#algebraic-geometry #arithmetic-geometry

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