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7 papers
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…
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…
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…
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…