Journal of the Ramanujan Mathematical Society

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Endomorphism Algebras of Hyperelliptic Jacobians and Finite Projective Lines


Affiliations
1 Institute of Mathematics, Hebrew University of Jerusalem, Givat Ram, Jerusalem-91904, Israel
2 Department of Mathematics, Pennsylvania State University, University Park, PA-16802, United States
     

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Let K be a field with char (K)≠2. Let us fix an algebraic closure Ka of K. Let us put Gal(K):=Aut(Ka/K). If X is an abelian variety of positive dimension over Ka then we write End(X) for the ring of all its Ka-endomorphisms and End0(X) for the corresponding (semisimple finite-dimensional) ℚ-algebra End(X)⊗ℚ. We write End K(X) for the ring of all K-endomorphisms of X and End0K(X) for the corresponding (semisimple finite-dimensional) ℚ-algebra EndK(X)⊗ℚ.
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  • Endomorphism Algebras of Hyperelliptic Jacobians and Finite Projective Lines

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Authors

Arsen Elkin
Institute of Mathematics, Hebrew University of Jerusalem, Givat Ram, Jerusalem-91904, Israel
Yuri G. Zarhin
Department of Mathematics, Pennsylvania State University, University Park, PA-16802, United States

Abstract


Let K be a field with char (K)≠2. Let us fix an algebraic closure Ka of K. Let us put Gal(K):=Aut(Ka/K). If X is an abelian variety of positive dimension over Ka then we write End(X) for the ring of all its Ka-endomorphisms and End0(X) for the corresponding (semisimple finite-dimensional) ℚ-algebra End(X)⊗ℚ. We write End K(X) for the ring of all K-endomorphisms of X and End0K(X) for the corresponding (semisimple finite-dimensional) ℚ-algebra EndK(X)⊗ℚ.