Any measure preserving endomorphism generates both a decreasing sequence of σ-algebras and an invertible extension. In this paper we exhibit a dyadic measure preserving endomorphism (X, T, μ) such that the decreasing sequence of σ-algebras that it generates is not isomorphic to the standard decreasing sequence of σ-algebras. However the invertible extension is isomorphic to the Bernoulli two sh...

In this paper, we study the structure of Fano fibrations varieties admitting an int-amplified endomorphism. We prove that if a normal Q-factorial klt projective variety X has endomorphism, then there exists étale in codimension one finite morphism X˜?X such X˜ is type over its Albanese variety. As corollary, further assume smooth and rationally connected, type.

Let α : G → G be an endomorphism of a discrete amenable group such that [G : α(G)] < ∞. We study the structure of the C∗ algebra generated by the left convolution operators acting on the left regular representation space, along with the isometry of the space induced by the endomorphism.

We prove that the mass endomorphism associated to the Dirac operator on a Riemannian manifold is non-zero for generic Riemannian metrics. The proof involves a study of the mass endomorphism under surgery, its behavior near metrics with harmonic spinors, and analytic perturbation arguments.

Assuming the continuum hypothesis, we construct a pure subgroup G of the Baer–Specker group Zא0 with the following properties. Every endomorphism of G differs from a scalar multiplication by an endomorphism of finite rank. Yet G has uncountably many homomorphisms to Z.

It is shown that a complex normal projective variety has non-positive Kodaira dimension if it admits a non-isomorphic quasi-polarized endomorphism. The geometric structure of the variety is described by methods of equivariant lifting and fibrations. Endomorphisms of the projective spaces are also discussed and some results on invariant subvarieties under the pullback of the endomorphism are obt...

Consider the Jacobian of a hyperelliptic genus two curve de ned over a nite eld. Under certain restrictions on the endomorphism ring of the Jacobian, we give an explicit description of all non-degenerate, bilinear, anti-symmetric and Galois-invariant pairings on the Jacobian. From this description it follows that no such pairing can be computed more e ciently than the Weil pairing. To establish...

Part I gives algebraic basic notions necessary to generating a graded sheaf of rings from a Galois extension, i.e. essentially a specialization, called emergent, from a ring of polynomials A[x1, ..., xm] giving rise to a set of compact connected algebraic subgroups which correspond to the different sections of the sheaf of rings θ. Part II refers to the introduction of the Eisenstein homology b...

We introduce the endomorphism distinguishing number De(G) of a graph G as the least cardinal d such that G has a vertex coloring with d colors that is only preserved by the trivial endomorphism. This generalizes the notion of the distinguishing number D(G) of a graph G, which is defined for automorphisms instead of endomorphisms. As the number of endomorphisms can vastly exceed the number of au...

It is conjectured that there exist finitely many isomorphism classes of simple endomorphism algebras of abelian varieties of GL2-type over Q of bounded dimension. We explore this conjecture when particularized to quaternion endomorphism algebras of abelian surfaces by giving a moduli interpretation which translates the question into the diophantine arithmetic of Shimura curves embedded in Hilbe...