Related papers: The Andre-Oort conjecture

In this paper we give an alternative, purely Conley index based proof of the Arnold conjecture in $\mathbb C\mathbb P^n$ asserting that a Hamiltonian diffeomorphism of $\mathbb C\mathbb P^n$ endowed with the Fubini-Study metric has at least…

We provide a simple proof for the union-closed sets conjecture, a long-standing open problem in set theory with immediate applications to graph theory, number theory, and order-theory.

We describe the set of points of the trianguline variety over a given local Galois representation. Global analogues describing companion points in eigenvariety by [Bre14] and [HN17], can be thought of as a rational analogue to the weight…

On montre comment les conjectures d'Arthur permettent de calculer les points de r\'eductibilit\'e pour les induites de cuspidales des groupes classiques. Les conjectures d'Arthur utilis\'ees portent sur l'existence d'un rel\`evement faible…

Given an odd prime number $p$ and a $p$-stabilized Artin representation $\rho$ over $\mathbb{Q}$, we introduce a family of $p$-adic Stark regulators and we formulate an Iwasawa-Greenberg main conjecture and a $p$-adic Stark conjecture which…

We prove special cases of a general conjecture: If an invertible field theory admits a projectively topological boundary theory, then it has finite order in the abelian group of invertible field theories. One can substitute `gapped' for…

We give a generalization to higher dimensions of Silverman's result on finiteness of integer points in orbits. Assuming Vojta's conjecture, we prove a sufficient condition for morphisms on P^N so that (S,D)-integral points in each orbit are…

In this note, we show that any epimorphism originating at a von Neumann regular ring (not necessary commutative) is a universal localization. As an application, we prove that the Telescope Conjecture holds for the unbounded derived…

We give conditions under which the monodromy group of an $A$-hypergeometric system is invariant under modifications of the collection of characters $A$. The key ingredient is a Zariski--Lefschetz type theorem for principal $A$-determinants.

In this article, we give proofs on the Arnold Lagrangian intersection conjecture on the cotangent bundles, Arnold-Givental Lagrangian intersection conjecture and the Arnold fixed point conjecture.

We prove the Arnold chord conjecture on cotangent bundles of open manifold by Gromov's nonlinear Fredholm alternative for $J-$holomorphic curves.

We use the Gromov-Witten invariants and a nonsqueezing theorem by the author to affirm a conjecture by P.Biran on the Lagrangian barriers.

We study the dependence on various parameters of the exceptional set in Vojta's conjecture. In particular, by making use of certain elliptic surfaces, we answer in the negative the often-raised question of whether Vojta's conjecture holds…

Several results about the union-closed sets conjecture are presented.

We study the Toda conjecture of Eguchi and Yang for the Gromov-Witten invariants of CP^1,using the bihamiltonian method of the formal calculus of variations. We also study its relationship to the Virasoro conjecture for CP^1, recently…

Let K be a finitely generated field over Q, and A an abelian variety over K. Let <, > : A(K^a) x A(K^a) --> R be an arithmetic height pairing on A, where K^a is the algebric closure of K. For x_1,..., x_l \in A(K^a), we denote det(<x_i,…

In \textit{Shimuravariet\"{a}ten und Gerben} \cite{LR87}, Langlands and Rapoport developed the theory of pseudo-motivic Galois gerb and admissible morphisms between Galois gerbs, with a view to formulating a conjectural description of the…

Let $G$ be a split $p$-adic reductive group with connected centre and simply connected derived subgroup. We show that certain "chains" of principal series of $G$ do not exist and we establish several properties of the Breuil-Herzig…

Let $k$ be algebraically closed field of characteristic zero, let $G$ be a commutative algebraic group over $k$ such that the linear part of $G$ is isomorphic to $\mathbb{G}_a$, and let $X$ be a closed subvariety of $G$. We show that the…

We give a new definition -- and in some cases, a new construction -- of integral canonical models of Shimura varieties that uses the notion of an aperture appearing in work of Gardner--Madapusi on some conjectures of Drinfeld. This applies…