Related papers: Algebraic cobordism via spans
We connect the homotopy type of simplicial moduli spaces of algebraic structures to the cohomology of their deformation complexes. Then we prove that under several assumptions, mapping spaces of algebras over a monad in an appropriate…
The construction of double point cobordism groups of vector bundles on varieties in the work [Lee-P] (arXiv:1002.1500 [math.AG]) of Yuan-Pin Lee and Rahul Pandharipande gives immediately double point cobordism groups of filtered vector…
We define parametrized cobordism categories and study their formal properties as bivariant theories. Bivariant transformations to a strongly excisive bivariant theory give rise to characteristic classes of smooth bundles with strong…
In this article, we study criteria for producing six-functor formalisms and morphisms between them. One notable application is that the motivic homotopy theory of algebraic stacks is the universal six-functor functor formalism in a strong…
Motivated by gauge theory, we develop a general framework for chain complex valued algebraic quantum field theories. Building upon our recent operadic approach to this subject, we show that the category of such theories carries a canonical…
We introduce a notion of regularity for coherent sheaves on Grassmannians of lines. We use this notion to prove some extension of Evans-Griffith criterion to characterize direct sums of line bundles. We also give a cohomological…
Under certain conditions, a scheme can be reconstructed from its category of quasi-coherent sheaves. The Tannakian reconstruction theorem provides another example where a geometric object can be reconstructed from an associated category, in…
We prove the formality theorem for the differential graded Lie algebra module of Hochschild chains for the algebra of endomorphisms of a smooth vector bundle. We discuss a possible application of this result to a version of the algebraic…
In his fundamental work, Quillen developed the theory of the cotangent complex as a universal abelian derived invariant, and used it to define and study a canonical form of cohomology, encompassing many known cohomology theories. Additional…
We give a new proof of an index theorem for fiber bundles of compact topological manifolds due to Dwyer, Weiss, and Williams, which asserts that the parametrized $A$-theory characteristic of such a fiber bundle factors canonically through…
Modular functors are traditionally defined as systems of projective representations of mapping class groups of surfaces that are compatible with gluing. They can formally be described as modular algebras over central extensions of the…
We classify the homotopy classes of proper Fredholm maps from an infinite dimensional Hilbert manifold into its model space in terms of a suitable version of framed cobordism. Our construction is an alternative approach to the…
We generalize the notion of a bornology by omitting the condition that a one-point-subset is bounded and obtain a complete and co-complete generalization of the category of bornological coarse spaces. Then we imitate the construction of…
Using an appropriate notion of locally convex Kasparov modules, we show how to induce isomorphisms under a large class of functors on the category of locally convex algebras; examples are obtained from spectral triples. Our considerations…
We show that the space of sections of any line bundle on the augmented wonderful variety of a hyperplane arrangement has the structure of a coalgebra. These coalgebras correspond to the hyperplane arrangement power ideals of Ardila and…
We prove a generalization of the fundamental theorem of algebraic K-theory for Verdier-localizing functors by extending the proof for algebraic K-theory of spaces to the realm of stable $\infty$-categories. The formula behaves much better…
We develop a categorical and algebro-geometric treatment of localization for cohomological theories endowed with an open--closed recollement. Starting from a class on a space whose restriction to the open complement vanishes, we show that…
We develop a functorial approach to the study of $n$-abelian categories by reformulating their axioms in terms of their categories of finitely presented functors. Such an approach allows the use of classical homological algebra and…
In [1] we introduced the concept of structured space, which is a topological space that locally resembles some algebraic structures. In [2] we proceeded the study of these spaces, developing two cohomology theories. The aim of this paper is…
Let $K$ be a sub-$p$-adic field. We show that the functor sending a finite type $K$-scheme to its \'etale topos is fully faithful after localizing at the class of universal homeomorphisms. This generalizes a result of Voevodsky, who proved…