Related papers: 3-nilpotent obstructions to pi_1 sections for P^1_…

Using the obstruction theory of Blanc-Dwyer-Goerss, we compute the moduli space of realizations of 2-stage Pi-algebras concentrated in dimensions 1 and n or in dimensions n and n+1. The main technical tools are Postnikov truncation and…

We consider families of abelian Galois coverings of the line. When the Jacobian of the general element is totally decomposable, i.e., is isogenous to a product of elliptic curves, we prove that they yield special subvarieties of $\A_g$ if…

Given a prime number l greater than or equal to 5, we construct an infinite family of three-dimensional abelian varieties over Q such that, for any A/Q in the family, the Galois representation \rho_{A, l}: Gal_Q -> GSp(6, l) attached to the…

Inspired by experimental data, this paper investigates which isogeny classes of abelian varieties defined over a finite field of odd characteristic contain the Jacobian of a hyperelliptic curve. We provide a necessary condition by…

In this article we prove that the elliptic, hyperbolic and nilpotent (or unipotent) additive (or multiplicative) Jordan components of an endomorphism $X$ (or an isomorphism $g$) of a finite dimensional vector space are given by polynomials…

In this preprint we present an outline of the multidimensional version of topological Galois theory. The theory studies topological obstruction to solvability of equations "in finite terms" (i.e. to their solvability by radicals, by…

We present two explicit recursions which determine the elliptic Gromov-Witten invariants of CP^3 in terms of the rational ones, and give a table up to degree 5. Unlike the rational Gromov-Witten invariants, the coefficients are negative and…

Let G(K) be the group of K-rational points of a connected adjoint simple algebraic group defined over a non-archimedean local field K. In this paper we classify the unipotent representations of G(K) in terms of the geometry of the Langlands…

We find new obstructions to the existence of complete Riemannian metric of nonnegative sectional curvature on manifolds with infinite fundamental groups. In particular, we construct many examples of vector bundles whose total spaces admit…

For finite p-groups P of class 2 and exponent p the following are invariants of fully refined central decompositions of P: the number of members in the decomposition, the multiset of orders of the members, and the multiset of orders of…

Let $k$ be a field of characteristic $0$. In this paper we describe a classification of smooth log K3 surfaces $X$ over $k$ whose geometric Picard group is trivial and which can be compactified into del Pezzo surfaces. We show that such an…

Let X be a smooth projective curve of genus >1 over a field K which is finitely generated over the rationals. The section conjecture in Grothendieck's anabelian geometry says that the sections of the canonical projection from the arithmetic…

We classify nilpotent Lie algebras with complex structures of weakly non-nilpotent type in real dimension eight, which is the lowest dimension where they arise. Our study, together with previous results on strongly non-nilpotent structures,…

We consider the canonical representation of the absolute Galois group of the rational numbers in the outer automorphism group of the pro-p completion of the fundamental group of the projective line minus 0,1, and infinity. Deligne has…

In this paper we investigate nilpotenct and probabilistically nilpotent Hopf algebras. We define nilpotency via a descending chain of commutators and give a criterion for nilpotency via a family of central invertible elements. These…

We study the possible weights of an irreducible 2-dimensional modular mod p representation of the absolute Galois group of F, where F is a totally real field which is totally ramified at p, and the representation is tamely ramified at the…

For any group $G$ containing an infinite elementary amenable subgroup, and any $2<p<\infty$, there exists closed invariant subspaces $E_i\nearrow \ell^pG$ and $F\neq 0$ such that $E_i\cap F = 0$ for all $i$. This is an obstacle to…

Given a genus two curve $X: y^2 = x^5 + a x^3 + b x^2 + c x + d$, we give an explicit parametrization of all other such curves $Y$ with a specified symplectic isomorphism on three-torsion of Jacobians $\mbox{Jac}(X)[3] \cong…

We study the proportion of metric matroids whose Jacobians have nontrivial $p$-torsion. We establish a correspondence between these Jacobians and the $\mathbb{F}_p$-rational points on configuration hypersurfaces, thereby relating their…

We study the behavior of geometric Picard ranks of K3 surfaces over the rationals under reduction modulo primes. We compute these ranks for reductions of smooth quartic surfaces modulo all primes $p<2^{16}$ in several representative…