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In this paper, we construct stable Bott--Samelson classes in the projective limit of the algebraic cobordism rings of full flag varieties, upon an initial choice of a reduced word in a given dimension. Each stable Bott--Samelson class is represented by a bounded formal power series modulo symmetric functions in positive degree. We make some explicit computations for those power series in the case of infinitesimal cohomology. We also obtain a formula of the restriction of Bott--Samelson classes to smaller flag varieties.
We prove that the $infty$-category of $mathrm{MGL}$-modules over any scheme is equivalent to the $infty$-category of motivic spectra with finite syntomic transfers. Using the recognition principle for infinite $mathbb{P}^1$-loop spaces, we deduce tha
We introduce the notion of flag Bott-Samelson variety as a generalization of Bott-Samelson variety and flag variety. Using a birational morphism from an appropriate Bott-Samelson variety to a flag Bott-Samelson variety, we compute Newton-Okounkov bod
We show that the motivic spectrum representing algebraic $K$-theory is a localization of the suspension spectrum of $mathbb{P}^infty$, and similarly that the motivic spectrum representing periodic algebraic cobordism is a localization of the suspensi
We obtain geometric models for the infinite loop spaces of the motivic spectra $mathrm{MGL}$, $mathrm{MSL}$, and $mathbf{1}$ over a field. They are motivically equivalent to $mathbb{Z}times mathrm{Hilb}_infty^mathrm{lci}(mathbb{A}^infty)^+$, $mathbb{
In the framework of the problem of characterizing complete flag manifolds by their contractions, the complete flags of type $F_4$ and $G_2$ satisfy the property that any possible tower of Bott-Samelson varieties dominating them birationally deforms i