33 citations · 58 across the 10 of their papers we have counts for
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Vector bundles on singular surfaces and threefolds
Jean Fasel, Maria Yakerson
We fully classify vector bundles of critical rank on normal affine surfaces and threefolds over algebraically closed fields via their Chern classes. We also prove existence of rank…
Twisted K-theory in motivic homotopy theory
Elden Elmanto, Denis Nardin, Maria Yakerson
In this paper, we study twisted algebraic -theory from a motivic viewpoint. For a smooth variety over a field of characteristic zero and an Azumaya algebra ove…
Hermitian K-theory via oriented Gorenstein algebras
Marc Hoyois, Joachim Jelisiejew, Denis Nardin +1
We show that the hermitian K-theory space of a commutative ring R can be identified, up to A^1-homotopy, with the group completion of the groupoid of oriented finite Gorenstein R-a…
The Hilbert scheme of infinite affine space and algebraic K-theory
Marc Hoyois, Joachim Jelisiejew, Denis Nardin +2
We study the Hilbert scheme from an -homotopical viewpoint and obtain applications to algebraic K-theory. We show that the Hilber…
On the infinite loop spaces of algebraic cobordism and the motivic sphere
Tom Bachmann, Elden Elmanto, Marc Hoyois +3
We obtain geometric models for the infinite loop spaces of the motivic spectra , , and over a field. They are motivically equivalent to $\m…
Modules over algebraic cobordism
Elden Elmanto, Marc Hoyois, Adeel A. Khan +2
We prove that the -category of -modules over any scheme is equivalent to the -category of motivic spectra with finite syntomic transfers. Using the re…
Towards conservativity of -stabilization
Tom Bachmann, Maria Yakerson
We study the interplay of the homotopy coniveau tower, the Rost-Schmid complex of a strictly homotopy invariant sheaf, and homotopy modules. For a strictly homotopy invariant sheaf…
Framed transfers and motivic fundamental classes
Elden Elmanto, Marc Hoyois, Adeel A. Khan +2
We relate the recognition principle for infinite -loop spaces to the theory of motivic fundamental classes of Déglise, Jin, and Khan. We first compare two kinds of tra…
Motivic infinite loop spaces
Elden Elmanto, Marc Hoyois, Adeel A. Khan +2
We prove a recognition principle for motivic infinite P1-loop spaces over a perfect field. This is achieved by developing a theory of framed motivic spaces, which is a motivic anal…
Algebraic K-theory of varieties , and their twisted forms
Maria Yakerson
Let , , , be simply connected split algebraic groups over an arbitrary field . Algebraic K-theory of affine homogeneous varie…