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A construction of an abelian variety with a given endomorphism algebra

F. Oort, M. Van der Put (1988)

Compositio Mathematica

A Family of Abelian Surfaces and Curves of Genus Four.

H. Lange, Ch. Birkenhake (1994)

Manuscripta mathematica

A Lefschetz decomposition for Chow motives of abelian schemes.

Klaus Künnemann (1993)

Inventiones mathematicae

A Note on height pairings on polarized abelian varieties

Valerio Talamanca (1999)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Let $A$ be an abelian variety defined over a number field $k$ . In this short Note we give a characterization of the endomorphisms that preserve the height pairing associated to a polarization. We also give a functorial interpretation of this result.

A Note on Height Pairings, Tamagawa Numbers, and the Birch and Swinnerton-Dyer Conjecture.

S. Bloch (1980)

Inventiones mathematicae

A note on minimal Galois embeddings of abelian surfaces

Hisao Yoshihara (2011)

Rendiconti del Seminario Matematico della Università di Padova

A series of smooth irregular varieties in projective space

Ciro Ciliberto, Klaus Hulek (1999)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Abelian surfaces of GL₂-type as Jacobians of curves

Josep González, Jordi Guàrdia, Victor Rotger (2005)

Acta Arithmetica

Abelian surfaces of type (1, 4).

H. Lange, C. Birkenhake (1989)

Mathematische Annalen

Abelian varieties and a conjecture of R.M. Robinson.

Manohar L. Madan, Sat Pal (1977)

Journal für die reine und angewandte Mathematik

Abelian varieties and curves in $W_{d} (C)$

Dan Abramovich, Joe Harris (1991)

Compositio Mathematica

Abelian varieties in $W_{d}^{r} (C)$ and points of bounded degree on algebraic curves

Olivier Debarre, Rachid Fahlaoui (1993)

Compositio Mathematica

Algebraic cycles in families of abelian varieties over Hilbert-Blumenthal surfaces.

B. Brent Gordon (1994)

Journal für die reine und angewandte Mathematik

Algebraic cycles on abelian varieties and their decomposition

Giambattista Marini (2004)

Bollettino dell'Unione Matematica Italiana

For an Abelian Variety $X$ , the Künneth decomposition of the rational equivalence class of the diagonal $Δ \subset X \times X$ gives rise to explicit formulas for the projectors associated to Beauville's decomposition (1) of the Chow ring $C H^{∙} (X)$ , in terms of push-forward and pull-back of $m$ -multiplication. We obtain a few simplifications of such formulas, see theorem (4) below, and some related results, see proposition (9) below.

Algebraic Cycles on Abelian Varieties of Fermat Type.

Tetsuji Shioda (1981)

Mathematische Annalen

Algebraic cycles on generic abelian varieties

Najmuddin Fakhruddin (1996)

Compositio Mathematica

Algebraic groups associated with abelian varieties.

Takashi Ichikawa (1991)

Mathematische Annalen

An explicit version of Faltings' Product Theorem and an improvement of Roth's lemma

Jan-Hendrik Evertse (1995)

Acta Arithmetica

An iterative construction for ordinary and very special hyperelliptic curves

Francis J. Sullivan (1983)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Si costruiscono famiglie di curve iperellittiche col $p$ —rango della varietà jacobiana uguale a zero. La costruzione sfrutta le proprietà elementari dell’operatore di Cartier e delle estensioni $p$ -cicliche dei corpi con la caratteristica $p$ maggiore di zero.

Arithmetic on curves of genus 1. VIII. On conjectures of Birch and Swinnerton-Dyer.

J.W.S. Cassels (1965)

Journal für die reine und angewandte Mathematik

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