Related papers: Chai's conjecture for semiabelian Jacobians

We prove a general theorem that gives a non trivial relation in the group of derived autoequivalences of a variety (or stack) X, under the assumption that there exists a suitable functor from the derived category of another variety Y…

In [19] we studied a Fadell-Neuwirth type fibration theorem for orbifolds, and gave a short exact sequence of fundamental groups of configuration Lie groupoids of Lie groupoids corresponding to the genus zero 2-dimensional orbifolds with…

We extend the Jacobi structure from $TQ\times \mathbb{R}$ and $T^{*}Q \times \mathbb{R}$ to $A\times \mathbb{R}$ and $A^{*}\times \mathbb{R}$, respectively, where $A$ is a Lie algebroid and $A^{*}$ carries the associated Poisson structure.…

Let $K$ be a field which is complete for a discrete valuation. We prove a logarithmic version of the N\'eron-Ogg-Shafarevich criterion: if $A$ is an abelian variety over $K$ which is cohomologically tame, then $A$ has good reduction in the…

Let $m\geq3$ be an integer. We show that every torsor of the Jacobian of the universal family of degree-$m$ Fermat curve is necessarily a connected component of the Picard scheme. We show that the Jacobian of the generic degree-$m$ Fermat…

We study {\em right-invariant (resp., left-invariant) Poisson quasi-Nijenhuis structures} on a Lie group $G$ and introduce their infinitesimal counterpart, the so-called {\em r-qn structures} on the corresponding Lie algebra $\mathfrak g$.…

We prove that the cohomology class of any curve on a very general principally polarized abelian variety of dimension at least 4 is an even multiple of the minimal class. The same holds for the intermediate Jacobian of a very general cubic…

In characteristic zero, semistable principal bundles on a nonsingular projective curve with a semisimple structure group form a bounded family, as shown by Ramanathan in 1970's using the Narasimhan-Seshadri theorem. This was the first step…

We construct examples of number fields which are not isomorphic but for which their idele class groups are isomorphic. We also construct examples of projective algebraic curves which are not isomorphic but for which their Jacobian varieties…

Let $L/K$ be an extension of complete discrete valuation fields, and assume that the residue field of $K$ is perfect and of positive characteristic. The residue field of $L$ is not assumed to be perfect. In this paper, we prove a formula…

We study a natural question in the Iwasawa theory of algebraic curves of genus $>1$. Fix a prime number $p$. Let $X$ be a smooth, projective, geometrically irreducible curve defined over a number field $K$ of genus $g>1$, such that the…

We consider the problem of constructing universal N\'eron models for families of curves with sections. By applying a construction of the author of universal compactified Jacobians over the moduli stack of reduced curves with markings and a…

Let E be an elliptic curve defined over a finite field. Balasubramanian and Koblitz have proved that if the l-th roots of unity m_l is not contained in the ground field, then a field extension of the ground field contains m_l if and only if…

In this paper, using a generalization of the notion of Prym variety for covers of quasi-projective varieties, we prove a structure theorem for the Mordell-Weil group of the abelian varieties over function fields that are twists of Abelian…

Assume that the section conjecture holds over number fields. We prove then that it holds for a broad class of curves defined over finitely generated extensions of $\mathbb{Q}$. This class contains every projective, hyperelliptic curve,…

One of the main results of this paper is a proof of the rank one case of an existence conjecture on lisse l-adic sheaves on a smooth variety over a finite field due to Deligne and Drinfeld. The problem is translated into the language of…

We generalize Keller's construction \cite{Kel11} of deformed $n$-Calabi-Yau completions to the relative context. This gives a construction that extends any given dg functor $F : A \rightarrow B$ between smooth dg categories to a dg functor…

We discuss an analogue of Riemann-Roch theorem for curves with an infinite number of handles. We represent such a curve X by its Shottki model, which is an open subset U of CP^{1} with infinite union of circles as a boundary. An appropriate…

Cais, Ellenberg and Zureick-Brown recently observed that over finite fields of characteristic two, all sufficiently general smooth plane projective curves of a given odd degree admit a non-trivial rational 2-torsion point on their Jacobian.…

The topic of this paper concerns a certain relation between the jacobians of various quotients of the modular curve $X(p)$, which relates the jacobian of the quotient of $X(p)$ by the normaliser of a non-split Cartan subgroup of $GL_2(F_p)$…