相关论文: On motivic decompositions arising from the method …

In this note, we describe motivic cell structures arising from the Bialynicki-Birula decomposition. This provides a description of the stable A^1-homotopy types of smooth projective G_m-varieties where the G_m-action has isolated fixed…

We generalize the Bia{\l}ynicki-Birula decomposition from actions of $G_m$ on smooth varieties to actions of linearly reductive group ${\bf G}$ on finite type schemes and algebraic spaces. We also provide a relative version and briefly…

Our goal in this work is to develop aspects of Bialynicki-Birula and Morse-Bott theory that can be extended from the classical setting of smooth manifolds to that of complex analytic spaces with a holomorphic $\mathbb{C}^*$ action. We…

Let $G$ be a semi-simple algebraic group over a perfect field $k$. A lot of progress has been made recently in computing the Chow motives of projective $G$-homogenous varieties. When $k$ has positive characteristic, a broader class of…

We provide a complete motivic decomposition of a twisted form of a smooth hyperplane section of Gr(3,6). This variety is a norm variety corresponding to a (3,3)-symbol.

We investigate several aspects of the Bialynicki-Birula decomposition of a smooth complete $\mathbb{G}_m$-variety with finite fixed locus. Our results include novel characterizations of when the Bialynicki-Birula decomposition is filterable…

We introduce the notion of Q-filtrable varieties: projective varieties with a torus action and a finite number of fixed points, such that the cells of the associated Bialynicki-Birula decomposition are all rationally smooth. Our main…

In this note, we give a general method to obtain unstable motivic cell structures, following Wendt's application of the Bialynicki-Birula algebraic Morse theory. We then apply the method to spherical varieties, with special attention to the…

We show that the motive of the Hilbert scheme of length-$n$ subschemes on a K3 surface or on an abelian surface admits a decomposition similar to the decomposition of the motive of an abelian variety obtained by Shermenev, Beauville, and…

We prove the existence of Bialynicki-Birula decomposition for Kempf monoids, which is a large class that contains for example monoids with reductive unit group in all characteristics. This extends the existence statements from previous…

We generalize some classical results on Chow group of an abelian variety to semiabelian varieties and to motivic (co)homology, using a result of Ancona--Enright-Ward--Huber on a decomposition of the motive of a semiabelian variety in the…

Over a perfect field k, let G be an extension of an abelian variety by the multiplicative group $\G_m$. We compute the motive of G in Voevodsky's category of etale motivic complexes with rational coefficients. The result is a decomposition…

These notes, written version of a Bourbaki talk, survey Morel-Voevodsky's motivic homotopy theory over a field, with a focus on computations of motivic homotopy sheaves, both stable and unstable. We also describe Isaksen-Wang-Xu's…

In this paper we explore the isotropic stable motivic homotopy category constructed from the usual stable motivic homotopy category, following the work of Vishik on isotropic motives (see [29]), by killing anisotropic varieties. In…

The aim of this work is to construct certain homotopy t-structures on various categories of motivic homotopy theory, extending works of Voevodsky, Morel, D\'eglise and Ayoub. We prove these $t$-structures possess many good properties, some…

In this paper, we continue the program initiated by Kahn-Saito-Yamazaki by constructing and studying an unstable motivic homotopy category with modulus, extending the Morel-Voevodsky construction from smooth schemes over a field $k$ to…

We apply Wildeshaus's theory of motivic intermediate extensions to the motivic decomposition conjecture, formulated by Deninger-Murre and Corti-Hanamura. We first obtain a general motivic decomposition for the Chow motive of an arbitrary…

We consider a complex smooth projective variety equipped with an action of an algebraic torus with a finite number of fixed points. We compare the motivic Chern classes of Bia{\l}ynicki-Birula cells with the $K$-theoretic stable envelopes…

We call the scheme parameterizing homogeneous ideals with fixed initial ideal the Gr\"obner scheme. We introduce a Bia{\l}ynicki-Birula decomposition of the Hilbert scheme $\mathrm{Hilb}^{P}_n$ for any Hilbert polynomial $P$ such that the…

We construct smooth presentations of algebraic stacks that are local epimorphisms in the Morel-Voevodsky $\mathbb{A}^1$-homotopy category. As a consequence we show that the motive of a smooth stack (in Voevodsky's triangulated category of…