Related papers: Hodge-Iwasawa Theory II

We extend the notion of rational points and cohomological obstructions on varieties to categories fibred in groupoids. We also establish the generalized theory of descent by torsors. Then we interpret the obstruction given by the second…

Iwasawa theory of Heegner points on abelian varieties of GL_2 type has been studied by, among others, Mazur, Perrin-Riou, Bertolini and Howard. The purpose of this paper, the first in a series of two, is to describe extensions of some of…

Dispersive deformations of the Monge equation u_u=uu_x are studied using ideas originating from topological quantum field theory and the deformation quantization programme. It is shown that, to a high-order, the symmetries of the Monge…

We argue that global F-theory compactifications to four dimensions generally exhibit higher rank Yukawa matrices from multiple geometric contributions known as Yukawa points. The holomorphic couplings furthermore have large hierarchies for…

Using geometric Eisenstein series, foundational work of Arinkin and Gaitsgory constructs cuspidal-Eisenstein decompositions for ind-coherent nilpotent sheaves on the de Rham moduli of local systems. This article extends these constructions…

In this article we show how the data of integrals of algebraic differential forms over algebraic cycles can be used in order to prove that algebraic and Hodge cycle deformations of a given algebraic cycle are equivalent. As an example, we…

We generalise Hinich's Theorem of descent of Deligne groupoids to the case where the dgLas involved have no negative cohomology. We apply this result to study the infinitesimal deformations of a morphism $\alpha: {\mathcal F} \to {\mathcal…

We shall develop a new deformation theory of geometric structures in terms of closed differential forms. This theory is a generalization of Kodaira -Spencer theory and further we obtain a criterion of unobstructed deformations. We apply…

We continue our study on the corresponding period rings with big coefficients, with the corresponding application in mind on relative $p$-adic Hodge theory and noncommutative analytic geometry. In this article, we extend the discussion of…

We study $p$-adic Hodge theory for families of Galois representations over pseudorigid spaces. Such spaces are non-archimedean analytic spaces which may be of mixed characteristic, and which arise naturally in the study of eigenvarieties at…

We survey recent advances in the theory of moduli spaces of stable sheaves on hyperk\"ahler manifolds of dimension greater than $2$. We start by recalling the well-known theory in dimension $2$, i.e.~for $K3$ surfaces, emphasizing the…

Our approach to higher order Fourier analysis is to study the ultra product of finite (or compact) Abelian groups on which a new algebraic theory appears. This theory has consequences on finite (or compact) groups usually in the form of…

We obtain variational formulas for holomorphic objects on Riemann surfaces with respect to arbitrary local coordinates on the moduli space of complex structures. These formulas are written in terms of a canonical object on the moduli space…

We fill a lacuna in the literature by giving a version in dimension 1 of the Relative Hurewicz Theorem, and relate this to abelianisations of groupoids, covering spaces and covering morphisms of groupoids, and Crowell's notion of derived…

Using bicomplex formalism we construct generalizations of Fordy-Kulish systems of matrix nonlinear Schroedinger equations on two-dimensional space-time in two respects. Firstly, we obtain corresponding equations in three space-time…

We conjecture a Verlinde type formula for the moduli space of Higgs sheaves on a surface with a holomorphic 2-form. The conjecture specializes to a Verlinde formula for the moduli space of sheaves. Our formula interpolates between…

We introduce a general theory of homological Milnor-Witt cycle modules over an excellent base scheme equipped with a dimension function, extending both Rost's cycle modules and Feld's theory over fields. To any such module we associate a…

We develop the deformation theory of cohomological field theories (CohFTs), which is done as a special case of a general deformation theory of morphisms of modular operads. This leads us to introduce two new natural extensions of the notion…

We completely calculate the Fitting ideal of the classical $p$-ramified Iwasawa module for any abelian extension $K/k$ of totally real fields, using the shifted Fitting ideals recently developed by the second author. This generalizes former…

We study the generic Hodge groups $\Hg(\sX)$ of local universal deformations $\sX$ of Calabi-Yau 3-manifolds with onedimensional complex moduli, give a complete list of all possible choices for $\Hg(\sX)_{\R}$ and determine the latter real…