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Points of elliptic curves over different fields

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#algebraic-geometry #extension-field #elliptic-curves #algebraic-groups #abelian-varieties
312
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For an isogeny of abelian varieties $f : X \to Y$, is $Y = X/ \operatorname{ker}f$?

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#algebraic-geometry #abelian-varieties
52
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What is the (geometic) genus of the image of curve under quotient map of its jacobian

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#algebraic-geometry #abelian-varieties
295
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Tate module of an Abelian Scheme

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#algebraic-geometry #elliptic-curves #arithmetic-geometry #abelian-varieties
311
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A natural isomorphism $\Omega_X \to T_{X,0}^* \otimes _k \mathscr{O}_X$ on an abelian variety $X$ (and the identification of vector fields)

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#algebraic-geometry #abelian-varieties
342
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On an abelian variety, every element of $\Omega_0 \otimes k$ extends to a holomorphisc differential form

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#algebraic-geometry #differential-forms #abelian-varieties
106
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division points of abelian varieties after reduction modulo a prime

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#abelian-varieties
243
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Points of Scholze's Anticanonical Tower

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#algebraic-geometry #modular-forms #arithmetic-geometry #abelian-varieties #automorphic-forms
109
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Is there a "Weierstrass form" for isogenies?

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#algebraic-geometry #elliptic-curves #cubics #abelian-varieties
612
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If isogenous elliptic curves have equal numbers of points, how can isogenies have non-trivial kernels?

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#finite-fields #elliptic-curves #abelian-varieties
451
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An abelian variety not isogenous to a Jacobian

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#algebraic-geometry #algebraic-number-theory #finite-fields #arithmetic-geometry #abelian-varieties
712
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Finding a kernel generator of the dual isogeny

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#elliptic-curves #cryptography #abelian-varieties
242
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What's the canonical definition of isogeny between semi-abelian schemes over base scheme S?

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#algebraic-geometry #flatness #abelian-varieties
92
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Morphism of algebraic groups defined over real points

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#reference-request #algebraic-groups #abelian-varieties
101
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Does every closed subgroup of an abelian variety have a direct complement?

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#algebraic-geometry #reference-request #abelian-varieties

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