Endomorphism algebras of Jacobians

Quasicompact and Riesz unital endomorphisms of real Lipschitz algebras of complex-valued functions

We first show that a bounded linear operator $ T $ on a real Banach space $ E $ is quasicompact (Riesz, respectively) if and only if $T': E_{mathbb{C}}longrightarrow E_{mathbb{C}}$ is quasicompact  (Riesz, respectively), where the complex Banach space $E_{mathbb{C}}$ is a suitable complexification of $E$ and $T'$ is the complex linear operator on $E_{mathbb{C}}$ associated with $T$. Next, we pr...

HOMOMORPHISMS OF ABELIAN VARIETIES by Yuri

— We study Galois properties of points of prime order on an abelian variety that imply the simplicity of its endomorphism algebra. Applications of these properties to hyperelliptic jacobians are discussed. Résumé (Homomorphismes des variétés abéliennes). — Nous étudions les propriétés galoisiennes des points d’ordre fini des variétés abéliennes qui impliquent la simplicité de leur algèbre d’end...

APPROXIMATELY INNER sigma-DYNAMICS ON C* ALGEBRAS

Endomorphism Algebras of Hyperelliptic Jacobians and Finite Projective Lines Arsen Elkin and Yuri G. Zarhin

Let K be a field with char(K) 6= 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 End (X) for the corresponding (semisimple finite-dimensional) Q-algebra End(X)⊗ Q. We write EndK(X) for the ring of all K-endomorphisms of X and End 0 K(X) for the c...

Comments on Gentleness of Endomorphism Algebras

In a joint paper with Jan Schröer we have shown that a module M over a special biserial algebra A with ExtA(M, M) = 0 has gentle stable endomorphism algebra. In the present note we interpret this result and study the gentle algebras which occur as stable endomorphism algebras of modules over the alternating group of degree 4 in characteristic 2.