Related papers: Abelian varieties with isogenous reductions

We consider homogeneity properties of Boolean algebras that have nonprincipal ultrafilters which are countably generated.It is shown that a Boolean algebra B is homogeneous if it is the union of countably generated nonprincipal ultrafilters…

We study deformations of complex projective varieties that are homotopically or homologically trivial. We formulate several conjectures and give some examples and partial answers.

The main result of [FG20] classifies the 92 geometric endomorphism algebras of geometrically split abelian surfaces defined over Q. We show that 54 of them arise as geometric endomorphism algebras of Jacobians of genus 2 curves defined over…

Let A be an abelian variety over a local field K of mixed characteristic and with algebraically closed residue field. We provide a geometric construction (via the relative Picard functor) of the Shafarevich duality between the group of…

Fix a prime number $\ell$. Graphs of isogenies of degree a power of $\ell$ are well-understood for elliptic curves, but not for higher-dimensional abelian varieties. We study the case of absolutely simple ordinary abelian varieties over a…

In this paper we introduce new affine algebraic varieties whose points correspond to associative algebras. We show that the algebras within a variety share many important homological properties. In particular, any two algebras in the same…

In this short note we study the questions of (non-)L-equivalence of algebraic varieties, in particular, for abelian varieties and K3 surfaces. We disprove the original version of a conjecture of Huybrechts \cite[Conjecture 0.3]{H} stating…

We analyze the relationship between abelian fourfolds of Weil type and Hodge structures of type K3, and we extend some of these correspondences to the case of arbitrary dimension.

The main aim of this paper is to classify the distinct multiplicative Lie algebra structures (up to isomorphism) on a given group. We also see that for a given group $G$, every homomorphism from the non-abelian exterior square $G \wedge G$…

If T is an algebraic torus defined over a discretely valued field K with perfect residue field k, we relate the K-cohomology of T to the k-cohomology of certain objects associated to T. When k has cohomological dimension <= 1, our results…

For any subfield K of the complex numbers which is not contained in an imaginary quadratic number field, we construct conjugate varieties whose algebras of K-rational (p,p)-classes are not isomorphic. This compares to the Hodge conjecture…

For a given abelian group G, we classify the isomorphism classes of G-gradings on the simple Lie algebras of types A_n (n >= 1), B_n (n >= 2), C_n (n >= 3) and D_n (n > 4), in terms of numerical and group-theoretical invariants. The ground…

In characteristic zero, it was proven a long time ago by D. Lieberman that cohomological and numerical equivalence coincide for cycles on abelian varieties. In this paper we show this to be true also in a somewhat technical sense for…

For g a split semisimple Lie algebra over a field of characteristic 0, we link locally trivial principal homogeneous spaces over Spec(R) to the question of conjugacy of maximal abelian diagonalizable subalgebras of g(R).

For an Abelian group $G$, any homomorphism $\mu\colon G\otimes G\rightarrow G$ is called a \textsf{multiplication} on $G$. The set $\text{Mult}\,G$ of all multiplications on an Abelian group $G$ is an Abelian group with respect to addition.…

A precise and testable modularity conjecture for rational abelian surfaces A with trivial endomorphisms, End_Q A = Z, is presented. It is consistent with our examples, our non-existence results and recent work of C. Poor and D. S. Yuen on…

Let A be an abelian threefold defined over a number field K with potential multiplication by an imaginary quadratic field M. If A has signature (2,1) and the multiplication by M is defined over an at most quadratic extension, we attach to A…

The main result of this paper is a characterization of the abelian varieties $B/K$ defined over Galois number fields with the property that the zeta function $L(B/K;s)$ is equivalent to the product of zeta functions of non-CM newforms for…

This paper gives a conjectural characterization of those elliptic curves over the field of complex numbers which "should" be covered by standard modular curves. The elliptic curves in question all have algebraic j-invariant, so they can be…

An abelian surface $A_{/{\mathbb Q}}$ of prime conductor $N$ is favorable if its 2-division field $F$ is an ${\mathcal S}_5$-extension with ramification index 5 over ${\mathbb Q}_2$. Let $A$ be favorable and let $B$ be any semistable…