Related papers: Generically log smooth families via generators and…

In order to understand the structure of the cohomologies involved in the study of projectively equivariant quantizations, we introduce a notion of affine representation of a Lie algebra.We show how it is related to linear representations…

We develop a theory of motives with compact support for logarithmic schemes over a field. Starting from the notion of finite logarithmic correspondences with compact support, we define the logarithmic motive with compact support analogous…

Let $G\subset GL(V)$ be a linear Lie group with Lie algebra $\frak g$ and let $A(\frak g)^G$ be the subalgebra of $G$-invariant elements of the associative supercommutative algebra $A(\frak g)= S(\frak g^*)\otimes \La(V^*)$. To any…

We review existing methods for implementing smooth functions f(A) of a sparse Hermitian matrix A on a quantum computer, and analyse a further combination of these techniques which has some advantages of simplicity and resource consumption…

In this paper, the Lawson homology and morphic cohomology are defined on the Chow motives. We also define the rational coefficient Lawson homology and morphic cohomology of the Chow motives of finite quotient projective varieties. As a…

Relations between some kinds of formal and standard smoothness, for morphisms of schemes, are clarified in surprisingly simple and direct ways, bypassing much of the customarily employed machinery. Even the deep local-to-global property of…

We give algorithms for the computation of the algebraic de Rham cohomology of open and closed algebraic sets inside projective space or other smooth complex toric varieties. The methods, which are based on Gr\"obner basis computations in…

A general framework is presented which unifies the treatment of wavelet-like, quasidistribution, and tomographic transforms. Explicit formulas relating the three types of transforms are obtained. The case of transforms associated to the…

By a map we mean a $2$-cell decomposition of a closed compact surface, i.e., an embedding of a graph such that every face is homeomorphic to an open disc. Automorphism of a map can be thought of as a permutation of the vertices which…

Let $V$ be a complete discrete valuation ring with residue field $\mathbb{F}$. We define a cyclic homology theory for algebras over $\mathbb{F}$, by lifting them to free algebras over $V$, which we enlarge to tube algebras and complete…

Let $\mathcal{L}$ be a finite-dimensional semisimple Lie algebra of rank $N$ over an algebraically closed field of characteristic $0$. Associated to $\mathcal{L}$ is a family of polynomial folding maps…

We show that for a smooth, projective variety X defined over a number field K, cyclic homology with coefficients in the ring of infinite adeles of K, provides the right theory to obtain, using the lambda-operations, Serre's archimedean…

For a flat $p$-adic formal family $S$ of log points over a complete discrete valuation ring with perfect residue field of mixed characteristics $(0,p)$ and for a simple normal crossing log scheme $X$ over an exact closed log subscheme of…

In this paper, we describe Galois covers of algebraic curves and their families by using local systems associated to push-forward of sheaves by the structure morphism. More precisely, if $f:C\to Y$, we consider the sheaves $f_*(\C)$. The…

In this text, we outline a theory of schemes associated with a site, which generalizes a variety of geometries, such as manifolds, schemes, analytic spaces, simplicial complexes, and more. We present an abstract process of gluing model…

Consider a smooth connected algebraic group $G$ acting on a normal projective variety $X$ with an open dense orbit. We show that Aut($X$) is a linear algebraic group if so is $G$; for an arbitrary $G$, the group of components of Aut($X$) is…

Algorithmicists are well-aware that fast dynamic programming algorithms are very often the correct choice when computing on compositional (or even recursive) graphs. Here we initiate the study of how to generalize this folklore intuition to…

For a closed negatively curved surface $(X,g)$ the flat trace of the geodesic Koopman operators $V_g^\tau f=f\circ G_g^\tau$ is the periodic orbit distribution \[ \mathrm{Tr}^{\flat}…

We show that a particular subfunctor of the relative logarithmic Picard functor for families of aligned, log semistable curves over a regular base scheme and smooth over an open dense subscheme of the base is representable by a smooth…

Analytic methods are emerging in solid and configuration modeling, while providing new insights into a variety of shape and motion related problems by exploiting tools from group morphology, convolution algebras, and harmonic analysis.…