Related papers: Explicit p-adic unit-root formulas for hypersurfac…

Given a family $X$ of complex varieties degenerating over a punctured disc, one is interested in computing related invariants called the motivic nearby fiber and the refined limit mixed Hodge numbers, both of which contain information about…

The Monodromy Conjecture asserts that if c is a pole of the local topological zeta function of a hypersurface, then exp(2\pi i c) is an eigenvalue of the monodromy on the cohomology of the Milnor fiber. A stronger version of the conjecture…

We compute Benois $\mathscr{L}$-invariants of weight $1$ cuspforms and of their adjoint representations and show how this extends Gross' $p$-adic regulator to Artin motives which are not critical in the sense of Deligne. Benois'…

This paper works out the structure of singular points of p-adic differential equations (i.e. differential modules over the ring of functions analytic in some annulus with external radius 1). Surprisingly results look like in the formal case…

In this paper we give an example of a noncongruence subgroup whose three-dimensional space of cusp forms of weight 3 has the following properties. For each of the four residue classes of odd primes modulo 8 there is a basis whose Fourier…

We prove that regular supercuspidal representations of $p$-adic groups are uniquely determined by their character values on very regular elements -- a special class of regular semisimple elements on which character formulae are very simple…

We develop further basic tools in the theory of continuous bounded cohomology of locally compact groups. We apply this tools to establish a Milnor-Wood type inequality in a very general context and to prove a global rigidity result which…

This paper provides the technical tools needed in ongoing work of the authors to compute p-adic \'etale Abel-Jacobi maps in order to obtain explicit reciprocity laws for GSp4. In particular, we define and study syntomic polynomial…

Presenting p-adic numbers as {\em deformations} of finite fields allows a better understanding of Frobenius lifts and their connection with p-derivations in the sense of Buium \cite{Buium-Main}. In this way "numbers {\em are} functions", as…

For the universal family of cyclic covers of projective spaces branched along hyperplane arrangements in general position, we consider its monodromy group acting on an eigen linear subspace of the middle cohomology of the fiber. We prove…

We first introduce global arithmetic cohomology groups for quasi-coherent sheaves on arithmetic varieties, adopting an adelic approach. Then, we establish fundamental properties, such as topological duality and inductive long exact…

We prove the conjectured compatibility of $p$-adic fundamental lines with specializations at motivic points for a wide class of $p$-adic families of $p$-adic Galois representations (for instance, the families which arise from $p$-adic…

The p-adic description of Higgs mechanism in TGD framework provides excellent predictions for elementary particle and hadrons masses ([email protected] 9410058-62). The gauge group of TGD is just the gauge group of the standard model so…

The main goal of this paper is to prove, in positive characteristic $p$, stability behavior for the graded Betti numbers in the periodic tails of the minimal resolutions of Frobenius powers of the homogeneous maximal ideals for very general…

We compute the first cohomology group of the symmetric algebra of the universal \'etale $p$-adic local system on the tower of coverings of Drinfeld's $p$-adic half-plane. The result takes a factorized form, using the $p$-adic Langlands…

We prove level raising results for $p$-adic automorphic forms on definite unitary groups $U(3)/\mathbb{Q}$ and deduce some intersection points on the eigenvariety. Let $l$ be an inert prime where the level subgroups varies, if there is a…

The notion of a $p$-adic superspace is introduced and used to give a transparent construction of the Frobenius map on $p$-adic cohomology of a smooth projective variety over $\zp$ (the ring of $p$-adic integers), as well as an alternative…

We give a new derivation of an identity due to Z. Rudnick and P. Sarnak about the $n$-level correlations of eigenvalues of random unitary matrices as well as a new proof of a formula due to M. Diaconis and P. Shahshahani expressing averages…

Given a set of inequalities determined by homogeneous forms, the following intertwined results are established: (1) the volume of the real semi-algebraic domain determined by these inequalities is explicitly determined; it is shown to be…

Let ${\mathrm G}$ be the group $({\rm GL}_{2}\times {\rm GU}(1))/{\rm GL}_{1}$ over a totally real field $F$, and let $\mathscr{X}$ be a Hida family for ${\rm G}$. Revisiting a construction of Howard and Fouquet, we construct an explicit…