Let X ⊂ PdK be Drinfeld’s upper half space over a finite extension K of Qp. We construct for every GLd+1-equivariant vector bundle F on PdK , a GLd+1(K)equivariant filtration by closed subspaces on the K-Fréchet H(X ,F). This gives rise by duality to a filtration by locally analytic GLd+1(K)-representations on the strong dual H(X ,F). The graded pieces of this filtration are locally analytic in...

For a fairly general reductive group G/Qp , we explicitly compute the space of locally algebraic vectors in the Breuil–Herzig construction (ρ)ord , for a potentially semistableBorel-valued representationρ ofGal(Q̄p/Qp). The point beingwedealwith thewhole representation, not just its socle—and we go beyond GLn(Qp). In the case of GL2(Qp), this relation is one of the key properties of the p-adic l...

We construct the motive of an algebraic stack in Nisnevich topology. For stacks which are locally quotient stacks, we give a presentation terms simplicial schemes. also show that for motivic cohomology agrees with Edidin-Graham-Totaro Chow groups integer coefficients.

A locally compact group G is compact if and only if L(G) is an ideal in L(G), and the Fourier algebra A(G) of G is an ideal in A(G)∗∗ if and only if G is discrete. On the other hand, G is discrete if and only if C0(G) is an ideal in C0(G)∗∗. We show that these assertions are special cases of results on locally compact quantum groups in the sense of J. Kustermans and S. Vaes. In particular, a vo...

In this paper, we briefly introduce different types of buildings such as spherical buildings, Euclidean buildings, twin buildings, R-buildings and describe some of their applications to many subjects: (1) differential geometry such as Mostow strong rigidity, rank rigidity of nonpositively curved manifolds, Margulis superrigidity, quasi-isometry rigidity, classification of isoparametric manifold...

We analyze the complexity of ascendant sequences in locally nilpotent groups, showing that if G is a computable locally nilpotent group and x0; x1; : : : ; xN 2 G, N 2 N, then one can always …nd a uniformly computably enumerable (i.e. uniformly 1) ascendant sequence of order type ! + 1 of subgroups in G beginning with hx0; x1; : : : ; xN iG, the subgroup generated by x0; x1; : : : ; xN in G. Th...

I present a general theory of overconvergent p-adic automorphic forms and eigenvarieties for connected reductive algebraic groups G whose real points are compact modulo centre, extending earlier constructions for forms of GLn due to Buzzard, Chenevier and Yamagami. This leads to some new phenomena, including the appearance of intermediate spaces of “semiclassical” automorphic forms; this gives ...

following the categorical approach to universal algebra through algebraic theories, proposed by f.~w.~lawvere in his phd thesis, this paper aims at introducing a similar setting for general topology. the cornerstone of the new framework is the notion of emph{categorically-algebraic} (emph{catalg}) emph{topological theory}, whose models induce a category of topological structures. we introduce t...

We classify locally stable maps from the 3-sphere to 4-space up to homotopy through locally stable maps. The equivalence class of a locally stable map f is determined by the isotopy type τ(f) of its framed singularity link, its generalized normal degree ν(f), and the algebraic number of cusps κ(f) of any generic extension of f to a map of the 4-disk into 5-space. Furthermore, relations between ...

In this paper, we generalize properties for single-valued functions in homotopy theory to multi-valued functions. We present new definitions such as locally m-pathwise connected, m-simply m-covering space, and regular space. apply some topological from algebraic topology the