Related papers: Algebraic Cobordism in mixed characteristic

For a reductive connected group or a finite group over a field of characteristic zero, we define an equivariant algebraic cobordism theory by a generalized version of the double point relation of Levine-Pandharipande. We prove basic…

Let S be an essentially smooth scheme over a field of characteristic exponent c. Let MGL and HZ denote the algebraic cobordism spectrum and the motivic cohomology spectrum over S, respectively. We show that the canonical map MGL/(a1, a2,…

In this article, we study and review some aspects of twisted cohomologies on algebraic and analytic varieties. We compared such cohomologies in both the algebraic and analytic categories and defined two types of twisting parameters in the…

The algebraic cobordism group of a scheme is generated by cycles that are proper morphisms from smooth quasiprojective varieties. We prove that over a field of characteristic zero the quasiprojectivity assumption can be omitted to get the…

We examine various versions of oriented cohomology and Borel-Moore homology theories in algebraic geometry and put these two together in the setting of an "oriented duality theory", a generalization of Bloch-Ogus twisted duality theory.…

We address the general classification problem of all stable associative product structures in the complex cobordism theory. We show how to reduce this problem to the algebraic one in terms of the Hopf algebra $S$ (the Landweber-Novikov…

We define the algebraic cobordism of $\infty$-categories equipped with universal line bundle data as an initial oriented functor in the associated span category. In the standard motivic framework, this recovers the Thom spectrum model…

Lazard showed in his seminal work "Groupes analytiques $p$-adiques" that for rational coefficients continuous group cohomology of $p$-adic Lie-groups is isomorphic to Lie-algebra cohomology. We refine this result in two directions: firstly…

We show that the Conjecture of Voevodsky concerning slices of the algebraic cobordism spectrum MGL implies a general statement about the slices of motivic Landweber spectra. In particular it confirms the possible approach suggested by…

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 that, over a field of characteristic 0, this extends the…

This work concerns the study of properties of a group of Koszul algebras coming from the toric ideals of a chordal bipartite infinite family of graphs (alternately, these rings may be interpreted as coming from determinants of certain…

In this paper, we introduce a category of graded commutative rings with certain algebraic morphisms, to investigate the cobordism category of plumbed 3-manifolds. In particular, we define a non-associative distributive algebra that gives…

This note discusses the cyclic cohomology of a left Hopf algebroid ($\times_A$-Hopf algebra) with coefficients in a right module-left comodule, defined using a straightforward generalisation of the original operators given by Connes and…

In this paper, we develop an enhancement of derived algebraic geometry to apply to $\mathbb{A}^1$-homotopy theory introduced by Morel and Voevodsky. We call the enhancement "motivic derived algebraic geometry". We shall actually formulate…

An algebraic version of a theorem due to Quillen is proved. More precisely, for a ground field k we consider the motivic stable homotopy category SH(k) of P^1-spectra equipped with the symmetric monoidal structure described in…

The dual motivic Steenrod algebra with mod $\ell$ coefficients was computed by Voevodsky over a base field of characteristic zero, and by Hoyois, Kelly, and {\O}stv{\ae}r over a base field of characteristic $p \neq \ell$. In the case $p =…

The aim of this note is to show that the Lagrangian cobordism group of a Weinstein sector is isomorphic to its middle-dimensional singular cohomology. As an application, a geometric description of Viterbo restriction for cobordism groups is…

This is a sequel to our previous paper of oriented bivariant theory [14]. In 2001 M. Levine and F. Morel constructed algebraic cobordism $\Omega_*(X)$ for schemes $X$ over a field $k$ in an abstract way and later M. Levine and R.…

We construct an equivariant algebraic cobordism theory for schemes with an action by a linear algebraic group over a field of characteristic zero.

In this short note, we give a new sufficient condition for a linear map from a product of copies of a field to endomorphisms of a finite dimensional vector space over the same field to be an algebra homomorphism. We expect that this result…