Related papers: Nonvanishing Higher Derived Limits without $w\diam…

We show that a totally degenerate limit of discrete series representation admits a choice of n-cohomology group that is nonvanishing at a canonically defined degree. We then show that these groups satisfy Serre duality. This produces two…

This paper studies the sliced nearby cycle functor and its commutation with duality. Over a Henselian discrete valuation ring, we show that this commutation holds, confirming a prediction of Deligne. As an application we give a new proof of…

We formulate and establish the central limit theorem for products of i.i.d. random variables on arbitrary simply connected nilpotent Lie groups, allowing a possible bias. Two new phenomena arise in the presence of a bias: (a) the walk…

We give a formalism of arithmetic mixed sheaves including the case of arithmetic mixed Hodge structures, and show the nonvanishing of certain higher extension groups, and also the nontriviality of the second Abel-Jacobi map for zero cycles…

We prove that under some conditions on the monodromy, families of abelian covers of the projective line do not give rise to (higher dimensional) Shimura subvarieties in $A_g$. This is achieved by a reduction to $p$ argument. We also use…

The existence of valuation domains admitting non-standard uniserial modules for which certain Exts do not vanish was proved under Jensen's Diamond Principle. In this note, the same is verified using the ZFC axioms alone.

We obtain nonvanishing estimates for central values of certain self-dual Rankin-Selberg $L$-functions on $\operatorname{GL}_2({\bf{A}}_F) \times \operatorname{GL}_2({\bf{A}}_F)$, and more generally $\operatorname{GL}_r({\bf{A}}_F) \times…

We prove that the set of exceptional $\lambda\in (1/2,1)$ such that the associated Bernoulli convolution is singular has zero Hausdorff dimension, and likewise for biased Bernoulli convolutions, with the exceptional set independent of the…

Consider groups such as Mordell-Weil groups of abelian varieties over number fields, odd algebraic $K$-theory groups of number fields, or finitely generated subgroups of the multiplicative groups of number fields. They are all equipped with…

A conjecture due to Y. Han asks whether that Hochschild homology groups of a finite dimensional algebra vanish for sufficiently large degrees would imply that the algebra is of finite global dimension. We investigate this conjecture from…

In this paper we address the relationship between Gromov-Hausdorff limits and intrinsic flat limits of complete Riemannian manifolds. In \cite{SormaniWenger2010, SormaniWenger2011}, Sormani-Wenger show that for a sequence of Riemannian…

In this paper we generalize the Deuring theorem on a reduction of elliptic curve with complex multiplication. More precisely, for an Abelian variety $A$, arising after reduction of an Abelian variety with complex multiplication by a CM…

We prove level-by-level upper and lower bounds on the strength of determinacy for finite differences of sets in the hyperarithmetical hierarchy in terms of subsystems of finite-and transfinite-order arithmetic, extending the…

We associate a family of ideal sheaves to any Q-effective divisor on a complex manifold, called higher multiplier ideals, using the theory of mixed Hodge modules and V-filtrations. This family is indexed by two parameters, an integer…

We show the non-vanishing of cohomology groups of sufficiently small congruence lattices in $SL(1,D)$, where $D$ is a quaternion division algebras defined over a number field $E$ contained inside a solvable extension of a totally real…

We prove a Generic Vanishing Theorem for coherent sheaves on an abelian variety over an algebraically closed field $k$. When $k=\CC$ this implies a conjecture of Green and Lazarsfeld.

We show that polarisations of type (1,...,1,2g+2) on g-dimensional abelian varieties are $\it{never}$ very ample, if $g\geq 3$. This disproves a conjecture of Debarre, Hulek and Spandaw. We also give a criterion for non-embeddings of…

In this paper, we extend the results of \cite{BCGS} on refined conjectures by Kurihara and Kolyvagin, allowing primes of any reduction type in the case of Kurihara's conjectures, and inert primes in the underlying imaginary quadratic field…

Let p=tp(a/A) be a stationary type in an arbitrary finite rank stable theory, and P an A-invariant family of partial types. The following property is introduced and characterised: whenever c is definable over (A,a) and a is not algebraic…

We obtain a local central limit theorem for cocycles associated with a class of non abelian and non compact group extensions of Gibbs Markov maps. This class consists of multidimensional infinite dihedral groups. Unlike in the set up of the…