Related papers: A note on the ring of invariant jet differentials

In this paper, we explore a ring invariant which is closely related to the Davenport constant of a group. In particular, we will calculate this invariant for a certain class of rings of integers and their orders and use it to understand…

We define pointwise partial differential relations for holomorphic discs. Given a relative homotopy class, a relation, and a generic almost complex structure we provide the moduli space of discs which have an injective point with the…

This article explains how to practically compute L-invariants of p-new eigenforms using p-adic L-series and exceptional zero phenomena. As proof of the utility, we compiled a data set consisting of over 150,000 L-invariants. We analyze…

We give an infinite dimensional description of the differential K-theory of a manifold $M$. The generators are triples $[H, A, \omega]$ where $H$ is a ${\bf Z}_2$-graded Hilbert bundle on $M$, $A$ is a superconnection on $H$ and $\omega$ is…

We discuss stationary discs for generic CR manifolds and apply them to the problem of finite jet determination for CR mappings. We prove that a CR diffeomorphism of two finitely smooth strictly pseudoconvex Levi generating CR manifolds is…

The object of study is the group of units O^\ast(X) in the coordinate ring of a normal affine variety X over an algebraically closed field k. Methods of Galois cohomology are applied to those varieties that can be presented as a finite…

For an infinity of number rings we express stable motivic invariants in terms of topological data determined by the complex numbers, the real numbers, and finite fields. We use this to extend Morel's identification of the endomorphism ring…

We prove that dg manifolds of finite positive amplitude, i.e. bundles of positively graded curved $L_\infty[1]$-algebras, form a category of fibrant objects. As a main step in the proof, we obtain a factorization theorem using path spaces.…

We construct highly singular projective curves and surfaces defined by invariants of primitive complex reflection groups.

We prove finite jet determination for (finitely) smooth CR diffeomorphisms of (finitely) smooth Levi degenerate hypersurfaces in $\mathbb{C}^{n+1}$ by constructing generalized stationary discs glued to such hypersurfaces.

For every odd prime number p, we give examples of non-constant smooth families of genus 2 curves over fields of characteristic p which have pro-Galois (pro-\'etale) covers of infinite degree with geometrically connected fibers. The…

Splitting invariants describe how a plane curve "splits" by the pull-back under a Galois cover over the projective plane whose branch locus contains no component of the plane curve. They enable us to distinguish the embedded topology of…

The well-known geometric approach to field theory is based on description of classical fields as sections of fibred manifolds, e.g. bundles with a structure group in gauge theory. In this approach, Lagrangian and Hamiltonian formalisms…

We present a way of constructing and deforming diffeomorphisms of manifolds endowed with a Lie group action. This is applied to the study of exotic diffeomorphisms and involutions of spheres and to the equivariant homotopy of Lie groups.

We generalize the main result of Demailly \cite{D2} for the bundles $E_{k,m}^{GG}(V^*)$ of jet differentials of order $k$ and weighted degree $m$ to the bundles $E_{k,m}(V^*)$ of the invariant jet differentials of order $k$ and weighted…

This article presents some computations for a new topological invariant for foliations introduced some years ago by the author using techniques from noncommutative geometry, in particular the pairing between K-Theory and cyclic cohomology.…

Let $K$ be a finite extension of $\mathbb{Q}_p$, and choose a uniformizer $\pi\in K$, and put $K_\infty:=K(\sqrt[p^\infty]{\pi})$. We introduce a new technique using restriction to $\Gal(\ol K/K_\infty)$ to study flat deformation rings. We…

We consider a problem whether a CR mapping of a generic manifold in complex space is uniquely determined by its finite jet at a point, which is referred to as finite jet determination. We derive the finite jet determination for CR mappings…

By analogy with algebraic geometry, we define a category of non-linear sheaves (quasi-coherent homotopy-sheaves of topological spaces) on projective toric varieties and prove a splitting result for its algebraic K-theory, generalising…

An interpretation of the formation of halo in accelerators based on quantum-like theory by a diffraction model is given in terms of the transversal beam motion. Physical implications of the longitudinal dynamics are also examined