Related papers: Torsion in Griffiths Groups

We generalize, for integral curves, a celebrated result of Max Noether on global sections of the n-dualizing sheaf of a smooth nonhyperelliptic curve. This is our main result. We also obtain an embedding of a non-Gorenstein curve in a way…

In this article, we investigate the possible torsion subgroups of twists of abelian varieties with good reduction. As an application, we prove a theorem concerning ramified primes over any quadratic extension where odd-order torsion growth…

A generalized Mordell curve of degree $n \ge 3$ over $\bQ$ is the smooth projective model of the affine curve of the form $Az^2 = Bx^n + C$, where $A, B, C$ are nonzero integers. A generalized Fermat curve of signature $(n, n, n)$ with $n…

Given an odd representation of the absolute Galois group of Q onto PGL(2,3) and a positive integer N, there exists a twisted modular curve defined over Q whose rational points classify the quadratic Q-curves of degree N realizing the…

Let $X$ be a compact smooth manifold, possibly with boundary. Denote by $X_1,\dots,X_r$ the connected components of $X$. Assume that the integral cohomology of $X$ is torsion free and supported in even degrees. We prove that there exists a…

Let $C$ be a hyperelliptic curve of genus $g>1$ over an algebraically closed field $K$ of characteristic zero and $O$ one of the $(2g+2)$ Weierstrass points in $C(K)$. Let $J$ be the jacobian of $C$, which is a $g$-dimensional abelian…

We classify the 5-dimensional homogeneous geometries in the sense of Thurston. The present paper (part 3 of 3) classifies those in which the linear isotropy representation is nontrivial but reducible. Most of the resulting geometries are…

We compute all the moments of the p-torsion in the first step of a filtration of the class group defined by Gerth for cyclic fields of degree p, unconditionally for p=3 and under GRH in general. We show that it satisfies a distribution…

In a group, a non-trivial element is called a generalized torsion element if some non-empty finite product of its conjugates equals to the identity. We say that a knot has generalized torsion if its knot group admits such an element. For a…

By a classical result of Roitman, a complete intersection $X$ of sufficiently small degree admits a rational decomposition of the diagonal. This means that some multiple of the diagonal by a positive integer $N$, when viewed as a cycle in…

We define the Grothendieck group of an n-angulated category and show that for odd n its properties are as in the special case of n=3, i.e. the triangulated case. In particular, its subgroups classify the dense and complete n-angulated…

For each prime $p$, we show that there exist geometrically simple abelian varieties $A/\mathbb Q$ with non-trivial $p$-torsion in their Tate-Shafarevich groups. Specifically, for any prime $N\equiv 1 \pmod{p}$, let $A_f$ be an optimal…

We give a function F(d,n,p) such that if K/Q_p is a degree n field extension and A/K is a d-dimensional abelian variety with potentially good reduction, then #A(K)[tors] is at most F(d,n,p). Separate attention is given to the prime-to-p…

We exhibit a new presentation of the (equilateral) Von Dyck groups $D(2,3,n), \ n\ge 3$, in terms of two generators of order $n$ satisfying three relations, one of which is Artin's braid relation. By dropping the relation which fixes the…

We show that if $P$ is a $PD_3$-complex and $g\in\pi_1(P)$ has finite order $>1$ and infinite centraliser then $\pi_1(P)$ retracts onto $Z/2Z\oplus\mathbb{Z}$. If $P$ is an irreducible closed 3-manifold then it follows from the Projective…

A classification theorem is given of smooth threefolds of $\Bbb P^5$ covered by a family of dimension at least three of plane integral curves of degree $d\geq 2.$ It is shown that for such a threefold $X$ there are two possibilities:…

The Resolution Theorem for Compact Abelian Groups is applied to show that the profinite subgroups of a finite-dimensional compact connected abelian group (protorus) which induce tori quotients comprise a lattice under intersection (meet)…

We classify finite-dimensional Nichols algebras over finite nilpotent groups of odd order in group-theoretical terms. The main step is to show that the conjugacy classes of such finite groups are either abelian or of type C; this property…

We construct finitely generated simple torsion-free groups with strong homological control. Our main result is that every subset of $\mathbb{N} \cup \{\infty\}$, with some obvious exceptions, can be realized as the set of dimensions of…

We establish a connection between torsion packets on curves of genus $2$ and pairs of elliptic curves realized as double covers of the projective line $\mathbb{P}_{x}^{1}$ that have many common torsion $x$-coordinates. This can be used to…