相关论文: Filtrations and Buildings

The principal aim of this note is to give an elementary proof of the fact that any two fiber functors of a Tannakian category are locally isomorphic. This builds on an idea of Deligne concerning scalar extensions of Tannakian categories and…

We make a first step towards categorification of the dendriform operad, using categories of modules over the Tamari lattices. This means that we describe some functors that correspond to part of the operad structure.

In \cite{FGLNP}, Fox, Gromov, Lafforgue, Naor and Pach, in a respond to a question of Gromov \cite{G}, constructed bounded degree geometric expanders, namely, simplical complexes having the affine overlapping property. Their explicit…

We define local fibration structures for real map germs with strictly positive dimensional discriminant: a local fibration structure over the complement of the discriminant, and a complete local fibration structure which includes the…

We develop new techniques for constructing model structures from a given class of cofibrations, together with a class of fibrant objects and a choice of weak equivalences between them. As a special case, we obtain a more flexible version of…

We establish a duality between flat affine group schemes and rigid tensor categories equipped with a neutral fiber functor (called Tannakian lattice), both defined over a Dedekind ring. We use this duality and the known Tannakian duality…

Let $G$ denote an adjoint semi-simple group over an algebraically closed field and $T$ a maximal torus of $G$. Following Contou-Carr\`ere [CC], we consider the Bott-Samelson resolution of a Schubert variety as a variety of galleries in the…

We recall the Tannaka construction for certain types of split monoidal functor into Vect_{k}, and remove the compactness restriction on the domain.

Starting from filters over the set of indices, we introduce structures in a product of sets where the coordinate sets have the given structures.

Functors with an instance of the Traversable type class can be thought of as data structures which permit a traversal of their elements. This has been made precise by the correspondence between traversable functors and finitary containers…

We construct a tower of fibrations approximating the derived mapping space between two simplicially enriched operads subject to mild conditions. The n-th stage of the tower is obtained by neglecting operations with more than n inputs. The…

Let $k$ be a perfect field. Assume that the characteristic of $k$ satisfies certain tameness assumptions \eqref{tameness}. Let $\mathcal O_{_n} := k\llbracket z_{_1}, \ldots, z_{_n}\rrbracket$ and set $K_{_n} := \text{Fract}~\cO_{_n}$. Let…

We introduce the sphere fibration for real map germs with radial discriminant and we address the problem of its equivalence with the Milnor-Hamm tube fibration. Under natural conditions, we prove the existence of open book structures with…

In this paper we study the problem of constructing non-trivial subtowers and supertowers of recursive towers of function fields over finite fields.

We construct a faithful and conservative functor from prisms to $C_{p^\infty}$-Tambara functors; in appropriate situations, this gives an algebraic description of $\underline\pi_0{\mathrm{TC}^-}$. We also present two integral variants using…

We bound the symmetry algebra of a vector distribution, possibly equipped with an additional structure, by the corresponding Tanaka algebra. The main tool is the theory of weighted jets.

We present a general theory of fractal transformations and show how it leads to a new type of method for filtering and transforming digital images. This work substantially generalizes earlier work on fractal tops. The approach involves…

A simple, yet unifying method is provided for the construction of tilings by tiles obtained from the attractor of an iterated function system (IFS). Many examples appearing in the literature in ad hoc ways, as well as new examples, can be…

We consider divisorial filtration on the rings of functions on hypersurface singularities associated with Newton diagrams and their analogues for plane curve singularities. We compute the multi-variable Poincar\'e series for the latter…

We construct a fractured structure, in the sense of Lurie, on the $\infty$-topos of condensed anima. This fractured structure allows us to better comprehend various properties of condensed anima - we use it to exhibit an explicit collection…