Related papers: Loops of Lie type: a p-adic example
We describe arbitrary multiplicative differential forms on Lie groupoids infinitesimally, i.e., in terms of Lie algebroid data. This description is based on the study of linear differential forms on Lie algebroids and encompasses many known…
We give an introduction to the "categorical" approach to the p-adic Langlands program, in both the "Banach" and "analytic" settings.
This is a survey on extended affine Lie algebras and related types of Lie algebras, which generalize affine Lie algebras.
$p$-adic Hodge Theory is one of the most powerful tools in modern Arithmetic Geometry. In this survey, we will review $p$-adic Hodge Theory for algebraic varieties, present current developments in $p$-adic Hodge Theory for analytic…
A Lie system is a system of differential equations admitting a superposition rule, i.e., a function describing its general solution in terms of any generic set of particular solutions and some constants. Following ideas going back to the…
We introduce operations with p-adic integer coefficients, associated to idempotents in the quantum cohomology of a monotone symplectic manifold, and apply them to the structure of the quantum connection.
This is a short presentation of some classical results on finite dimensional complex Lie algebras (classification of nilpotent Lie algebras, deformations and perturbations, contractions and rigidity). We present some applications to…
The aim of this work is to lay the foundations of differential geometry and Lie theory over the general class of topological base fields and -rings for which a differential calculus has been developed in recent work (collaboration with H.…
The aim of this paper is to propose an ``elementary" approach to Coleman's theory of p-adic abelian integrals. Our main tool is a theory of commutative p-adic Lie groups (the logarithm map); we use neither dagger analysis nor…
Hopf algebra structure on the differential algebra of the extended $q$-plane is defined. An algebra of forms which is obtained from the generators of the extended $q$-plane is introduced and its Hopf algebra structure is given.
The purpose of this work is to study Lie superalgebroid structures on the space of superdifferential $1$-forms over the supermanifolds whose superfunctions are the differential forms on its underlying manifold. These superalgbroids are…
We interpret and develop a theory of loop algebras as torsors (principal homogeneous spaces) over Laurent polynomial rings . As an application, we recover Kac's realization of affine Kac-Moody Lie algebras.
This text gives a construction of a differential graded Lie algebra in Nori's category of effective homological motives. In fact the construction works in more a general setting than that of an Abelian category. This allows us to give the…
We illustrate the theory of the radius of convergence of a connection on a p-adic curve X, by deducing from it a simple proof of a variant of Alain Robert's p-adic Rolle theorem. We need to carefully compare our global notion of radius of…
We discuss recent developments in $p$-adic geometry, ranging from foundational results such as the degeneration of the Hodge-to-de Rham spectral sequence for "compact $p$-adic manifolds" over new period maps on moduli spaces of abelian…
We present here "the" cartesian closed theory for real analytic mappings. It is based on the concept of real analytic curves in locally convex vector spaces. A mapping is real analytic, if it maps smooth curves to smooth curves and real…
We study \'etale descent of derivations of algebras with values in a module. The algebras under consideration are twisted forms of algebras over rings, and apply to all classes of algebras, notably associative and Lie algebras, such as the…
Lie theory is, beyond any doubt, an absolutely essential part of differential geometry. It is therefore necessary to seek its generalization to $\mathbb{Z}$-graded geometry. In particular, it is vital to construct non-trivial and explicit…
In this paper, we offer a brief introduction to the $p$-adic numbers and operations in the metric space defined under the $p$-adic norm. Specifically, we provide a clear description of the derivation of the $p$-adic number via the…
A Lie groupoid can be thought of as a generalization of a Lie group in which the multiplication is only defined for certain pairs of elements. From another perspective, Lie groupoids can be regarded as manifolds endowed with a type of…