9 citations · 22 across the 14 of their papers we have counts for
17 papers · 1 filter
Grothendieck ring of varieties and at-the-characteristic numerical invariants
Toni Annala, Matthew Satriano, Evan Sundbo
Assuming a weak form of resolution of singularities in positive characteristic, we show several at-the-characteristic numerical invariants, including Hodge numbers, are given by ho…
Motivic Steenrod operations at the characteristic via infinite ramification
Toni Annala, Elden Elmanto
We construct motivic power operations on the mod- motivic cohomology of $\Fb_p$-schemes using a motivic refinement of Nizioł's theorem. The key input is a purity theorem for mot…
Motivic Steenrod problem away from the characteristic
Toni Annala, Tobias Shin
In topology, the Steenrod problem asks whether every singular homology class is the pushforward of the fundamental class of a closed oriented manifold. Here, we introduce an analog…
Atiyah duality for motivic spectra
Toni Annala, Marc Hoyois, Ryomei Iwasa
We prove that Atiyah duality holds in the -category of non--invariant motivic spectra over arbitrary derived schemes: every smooth projective scheme is dualiza…
Algebraic cobordism and a Conner-Floyd isomorphism for algebraic K-theory
Toni Annala, Marc Hoyois, Ryomei Iwasa
We formulate and prove a Conner-Floyd isomorphism for the algebraic K-theory of arbitrary qcqs derived schemes. To that end, we study a stable -category of non-$\mathbb A^1…
Motivic spectra and universality of -theory
Toni Annala, Ryomei Iwasa
We develop a theory of motivic spectra in a broad generality; in particular -homotopy invariance is not assumed. As an application, we prove that -theory of scheme…
Derived Algebraic Cobordism
Toni Annala
We construct and study a theory of bivariant cobordism of derived schemes. Our theory provides a vast generalization of the algebraic bordism theory of characteristic 0 algebraic s…
Cohomology of the moduli stack of algebraic vector bundles
Toni Annala, Ryomei Iwasa
Let be the moduli stack of vector bundles of rank on schemes. We prove that, if is a Zariski sheaf of ring spectra which is equipped with finite…
Algebraic Spivak's theorem and applications
Toni Annala
We prove an analogue of Lowrey--Schürg's algebraic Spivak's theorem when working over a base ring that is either a field or a nice enough discrete valuation ring, and after inv…
Base independent algebraic cobordism
Toni Annala
The purpose of this article is to show that the bivariant algebraic -cobordism groups considered previously by the author are independent of the chosen base ring . This resul…
Precobordism and cobordism
Toni Annala
The purpose of this article is to compare several versions of bivariant algebraic cobordism constructed previously by the author and others. In particular, we show that a simple co…
Chern classes in precobordism theories
Toni Annala
We construct Chern classes of vector bundles in the universal precobordism theory of Annala--Yokura over an arbitrary Noetherian base ring of finite Krull dimension. As an immediat…
Bivariant algebraic cobordism with bundles
Toni Annala, Shoji Yokura
The purpose of this paper is to study an extended version of bivariant derived algebraic cobordism where the cycles carry a vector bundle on the source as additional data. We show…
On line bundles in derived algebraic geometry
Toni Annala
We give examples of derived schemes and a line bundle $\Ls$ on the truncation so that $\Ls$ does not extend to the original derived scheme . In other words the pullback…
Ample line bundles, global generation and on quasi-projective derived schemes
Toni Annala
The purpose of this note is to extend some classical results on quasi-projective schemes to the setting of derived algebraic geometry. Namely, we want to show that any vector bundl…
Bivariant derived algebraic cobordism
Toni Annala
We extend the derived Algebraic bordism of Lowrey and Schürg to a bivariant theory in the sense of Fulton and MacPherson, and establish some of its basic properties. As a special c…
Oriented Borel-Moore homologies of toric varieties
Toni Annala
We generalize the Künneth formula for Chow groups to an arbitrary OBM-homology theory satisfying descent (e.g. algebraic cobordism) when taking a product with a toric variety. As a…