Related papers: The mixed Tate property of reductive groups

In this paper we give a geometric construction of the Borel equivariant (co)homology for spaces with a $G$-action, where $G$ is a compact Lie group with the property that the adjoint representation is orientable. A nice feature of these…

We compute rationally the topological (complex) K-theory of the classifying space BG of a discrete group provided that G has a cocompact G-CW-model for its classifying space for proper G-actions. For instance word-hyperbolic groups and…

This is a sequel to our previous paper (joint with Furusho). It will give a more natural framework for constructing elements in the Hopf algebra of framed mixed Tate motives according to Bloch and Kriz. This framework allows us to extend…

This paper addresses the problem of describing the structure of tensor C*-categories M with conjugates and irreducible tensor unit. No assumption on the existence of a braided symmetry or on amenability is made. Our assumptions are…

The (maximal) Satake compactification associated to a real reductive group $G$ is the closure of the symmetric space of all maximal compact subgroups of $G$ within the compact space of all closed subgroups of $G$. We shall present three…

Let $G$ be a locally compact amenable group. We say that G has property (M) if every closed subgroup of finite covolume in G is cocompact. A classical theorem of Mostow ensures that connected solvable Lie groups have property (M). We prove…

We show that if G is a finite constant group acting on a scheme X such that the order of G is invertible in the residue fields of X, then the G-equivariant motivic stable homotopy category of X is equivalent to the stabilization of the…

For a family of group words $w$ we show that if $G$ is a profinite group in which all $w$-values are contained in a union of finitely many subgroups with a prescribed property, then $w(G)$ has the same property as well. In particular, we…

For a linear algebraic group $G$ over a field $k$, we define an equivariant version of the Voevodsky's motivic cobordism $MGL$. We show that this is an oriented cohomology theory with localization sequence on the category of smooth…

Let $E/\mathbb{Q}$ be a totally real number field that is Galois over $\mathbb{Q}$, and let $\pi$ be a cuspidal, nondihedral automorphic representation of $\mathrm{GL}_2(\mathbb{A}_E)$ that is in the lowest weight discrete series at every…

We construct the Chow weight structure on the derived category of geometric motives with arbitrary coefficients for X a finite type scheme over a field characteristic 0 and G an affine algebraic group. In particular we also show that the…

The motivation of this work is to construct an analog of compactified moduli of abelian varieties and toric pairs in the case of non-commutative algebraic group G. We introduce a class of "stable reductive varieties" which contain connected…

When the action of a reductive group on a projective variety has a suitable linearisation, Mumford's geometric invariant theory (GIT) can be used to construct and study an associated quotient variety. In this article we describe how…

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…

Mixed-parity module emerges for instance when a de Rham Galois representation is being tensored with a square root of cyclotomic character, which produces half odd integers as the corresponding Hodge-Tate weights. We build the whole…

In this paper we combine the principled approach to modalities from multimodal type theory (MTT) with the computationally well-behaved realization of identity types from cubical type theory (CTT). The result -- cubical modal type theory…

We study support $\tau$-tilting modules over preprojective algebras of Dynkin type. We classify basic support $\tau$-tilting modules by giving a bijection with elements in the corresponding Weyl groups. Moreover we show that they are in…

We investigate rational $G$-modules $M$ for a linear algebraic group $G$ over an algebraically closed field $k$ of characteristic $p > 0$ using filtrations by sub-coalgebras of the coordinate algebra $k[G]$ of $G$. Even in the special case…

We study the Chow groups and the Chow motives of the wonderful compactifications $Y_{\mathcal{G}}$ of arrangements of subvarieties. We prove a natural decomposition of the Chow motive of $Y_\mathcal{G}$, in particular of the…

We prove a deletion-contraction formula for motivic Feynman rules given by the classes of the affine graph hypersurface complement in the Grothendieck ring of varieties. We derive explicit recursions and generating series for these motivic…