Related papers: The higher Hilbert pairing via (phi,G)-modules

The field-of-norms functor is applied to deduce explicit reciprocity formulae for the Hilbert symbol in the mixed characteristic case from the explicit formula for the Witt symbol in characteristic p > 2 in the context of higher local…

We show that there exists a natural non-degenerate pairing of the homomorphism space between two neighbor standard modules over a quasi-hereditary algebra with the first extension space between the corresponding costandard modules and vise…

Using the theory of noncommutative symmetric functions, we introduce the higher order peak algebras, a sequence of graded Hopf algebras which contain the descent algebra and the usual peak algebra as initial cases (N = 1 and N = 2). We…

A field $K$ is $d$-local if there exist fields $K=k_d,...,k_0$ with $k_{i+1}$ complete discrete valuation with residue field $k_i$, and $k_0$ finite of characteristic $p$. By work of Deninger and Wingberg, the Galois cohomology of such…

Since the development of higher local class field theory, several explicit reciprocity laws have been constructed. In particular, there are formulas describing the higher-dimensional Hilbert symbol given, among others, by M. Kurihara, A.…

Let F be a totally real field and p a rational prime unramified in F. We prove a partial classicality theorem for overconvergent Hilbert modular forms: when the slope is small compared to certain but not all weights, an overconvergent form…

This first part of the paper describes the support of top graded local cohomology modules. As a corrolary one obtains a simple criteria for the vanishing of these modules and also the fact that they have finitely many minimal primes. The…

Using the previously constructed explicit reciprocity laws for the generalized Kummer pairing of an arbitrary (one-dimensional) formal group, in this article a special consideration is given to Lubin-Tate formal groups. In particular, this…

We give a proof of the Howe duality conjecture for the (almost) equal rank dual pairs in full generality. For arbitrary dual pairs, we prove the irreducibility of the (small) theta lifts for all tempered representations. Our proof works for…

We prove that a certain bilinear pairing (analagous to the Poincare-Lefschetz intersection pairing) between filtered sub- and quotient complexes of a Floer-type chain complex and of its "opposite complex" is always nondegenerate on…

Let $p$ be a prime and let $K$ be a finite extension of the field ${\bf Q}_p$ of $p$-adic numbers such that the group ${}_pK^\times$ has order $p$. The ${\bf F}_p$-space $K^\times\!/K^{\times p}$ carries a natural filtration coming from the…

We generalize the notion of harmonic conjugate functions and Hilbert transforms to higher dimensional euclidean spaces, in the setting of differential forms and the Hodge-Dirac system. These conjugate functions are in general far from being…

Let $A$ be an abelian variety defined over a number field $k$, let $p$ be an odd prime number and let $F/k$ be a cyclic extension of $p$-power degree. Under not-too-stringent hypotheses we give an interpretation of the $p$-component of the…

We use String Field Theory (SFT) to construct a higher analogue of Bunke-Schick's functor $P: \mathbf{Top}^{op} \to \mathbf{Set}$ \cite{BunkeS1} by geometrizing $P.$ We use the projection of SFT onto its massless modes \cite{SFTDiffeo} to…

Higher derivations on an associative algebra generalizes higher order derivatives. We call a tuple consisting of an algebra and a higher derivation on it by an AssHDer pair. We define a cohomology for AssHDer pairs with coefficients in a…

Let $S=K[x_1,\ldots,x_n]$ be the polynomial ring over the field $K$, and let $I\subset S$ be a graded ideal. It is shown that the higher iterated Hilbert coefficients of the graded $S$-modules $\Tor_i^S(M,I^k)$ and $\Ext^i_S(M,I^k)$ are…

For a rational prime $p \geq 3$ we consider $p$-ordinary, Hilbert modular newforms $f$ of weight $k\geq 2$ with associated $p$-adic Galois representations $\rho_f$ and $\mod{p^n}$ reductions $\rho_{f,n}$. Under suitable hypotheses on the…

We generalize the main result of arXiv:1206.6631 [math.NT] to all totally real fields. In other words, for $p>2$ prime, we prove (under a mild Taylor-Wiles hypothesis) that if a modular representation is unramified and $p$-distinguished at…

A field $K$ is quasi-classical $d$-local if there exist fields $K=k_d,\dots,k_0$ with $k_{i+1}$ Henselian admissible discretely valued with residue field $k_i$, and $k_0$ quasi-finite. We prove a duality theorem for the Galois cohomology of…

We equip the type $A$ diagrammatic Hecke category with a special derivation, so that after specialization to characteristic $p$ it becomes a $p$-dg category. We prove that the defining relations of the Hecke algebra are satisfied in the…