Related papers: Weak local-global compatibility and ordinary repre…

Let $F/F^+$ be a CM field and let $\widetilde{v}$ be a finite unramified place of $F$ above the prime $p$. Let $\overline{r}: \mathrm{Gal}(\overline{\mathbb{Q}}/F)\rightarrow \mathrm{GL}_n(\overline{\mathbb{F}}_p)$ be a continuous…

We establish a generic weak uniqueness result and partial regularity of the free boundary and of minimizers for the composite membrane problem.

We show that modular operads are equivalent to modules over a certain simple properad which we call the Brauer properad. Furthermore, we show that, in this setting, the Feynman transform corresponds to the cobar construction for modules of…

Let $\mathfrak{X}$ be a smooth connected $p$-adic formal scheme. Based on the prismatic description of crystalline local systems, we prove an analogue of Fontaine's conjecture for torsion crystalline local systems on the generic fiber of…

We construct projective varieties in mixed characteristic whose singularities model, in generic cases, those of tamely potentially crystalline Galois deformation rings for unramified extensions of $\mathbb{Q}_p$ with small regular…

In this paper, a general hybrid fixed point theorem for the contractive mappings in generalized Banach spaces is proved via measure of weak non-compactness and it is further applied to fractional integral equations for proving the existence…

We use a result of Hellus about generalized local duality to describe some generalized Matlis duals for certain quasi-\F-modules. Furthermore, we apply this description to obtain examples for non-artinian local cohomology modules by the…

We give an elementary proof of a generalization of Bourgain and Tzafriri's Restricted Invertibility Theorem, which says roughly that any matrix with columns of unit length and bounded operator norm has a large coordinate subspace on which…

We introduce a direct image formalism for constructible motivic functions. One deduces a very general version of motivic integration for which a change of variables theorem is proved. These constructions are generalized to the relative…

We generalise a theorem on the existence of Frobenius isocrystal and Fontaine-Laffaille module structures on rigid flat connections to the non-proper setting. The proof is based on a new strategy of a point-set topological flavour, which…

We estimate the proportion of function fields satisfying certain conditions which imply a function-field analogue of the Fontaine-Mazur conjecture. As a byproduct, we compute the fraction of abelian varieties (or even Jacobians) over a…

In this note, we are interested in local-global principles for multinorm equations of the form $\prod_{i=1}^n N_{L_i /k}(z_i) = a$ where $k$ is a global field, $L_i/k$ are finite separable field extensions and $a \in k^*$. In particular, we…

Given a programming language, can we give a monadic denotational semantics that is stable under language extension? Models containing only a single monad are not stable. Models based on type-and-effect systems, in which there is a monad for…

A necessary and sufficient condition is provided for the solvability of a binomial congruence with a composite modulus, circumventing its prime factorization. This is a generalization of Euler's Criterion through that of Euler's Theorem,…

In this paper, we prove the conjecture of Yui and Zagier concerning the factorization of the resultants of minimal polynomials of Weber class invariants. The novelty of our approach is to systematically express differences of certain Weber…

We survey some recent progress on generalizations of conjectures of Serre concerning the cohomology of arithmetic groups, focusing primarily on the "weight" aspect. This is intimately related to (generalizations of) a conjecture of Breuil…

In this paper, we define a generalization of the Brauer groups by using Bloch's cycle complex on etale site. We prove the Gersten conjecture of generalized Brauer group on some cases. As an application we prove the Gersten conjecture of the…

We give the geometric version of a construction of Colmez-Niziol which establishes a comparison theorem between arithmetic p-adic nearby cycles and syntomic sheaves. The local construction of the period isomorphism uses…

In this article we prove a version of Kolyvagin's conjecture for modular forms at non-ordinary primes. In particular, we generalize the work of Wang on a converse to a higher weight Gross-Zagier-Kolyvagin theorem in order to prove the…

Recently M. Mustata and V. Srinivas related a natural conjecture about the Frobenius action on the cohomology of the structure sheaf after reduction to characteristic $p > 0$ with another conjecture connecting multiplier ideals and test…