Related papers: Semi-topological K-theory for certain projective v…

We compute the semiflat positive cone $K_0^{+SF}(A_\theta^\sigma)$ of the $K_0$-group of the irrational rotation orbifold $A_\theta^\sigma$ under the noncommutative Fourier transform $\sigma$ and show that it is determined by classes of…

For $E$ a presheaf of spectra on the category of smooth $k$-schemes satisfying Nisnevich excision, we prove that the canonical map from the algebraic singular complex of the theory $E$ with quasi-finite supports to the theory $E$ with…

We extend Donaldson's asymptotically holomorphic techniques to symplectic orbifolds. More precisely, given a symplectic orbifold such that the symplectic form defines an integer cohomology class, we prove that there exist sections of large…

We construct and study a closed, two-dimensional, quasi-topological (0,2) gauged sigma model with target space a smooth G-manifold, where G is any compact and connected Lie group. When the target space is a flag manifold of simple G, and…

We study the question of the existence of a Waldhausen category on any (relative) abelian category in which the contractible objects are the (relatively) projective objects. The associated $K$-theory groups are "stable algebraic…

Let k be an algebraically closed field and X a smooth projective k-variety. A famous theorem of A. A. Roitman states that the canonical map from the degree zero part of the Chow group of zero cycles on X to the group of k-points of its…

Theorems of Barth-Lefschetz type describe restrictions on the topology of varieties of small codimension. R. Schoen and J. Wolfson, using Morse theory on a path space, have described a technique to prove theorems of this kind for complex…

In this paper, we study the algebraic analogue of the topological Atiyah-Segal completion theorem. We verify this completion theorem for the algebraic equivariant $K$-theory of smooth projective schemes. We also show that the completion…

In this short note we show that the homotopy category of smooth compactifications of smooth algebraic varieties is equivalent to the homotopy category of smooth varieties over a field of characteristic zero. As an application we show that…

We define the motivic filtrations on real topological Hochschild homology and its companions. In particular, we prove that real topological cyclic homology admits a natural complete filtration whose graded pieces are equivariant suspensions…

A particular case of Bergeron-Venkatesh's conjecture predicts that torsion classes in the cohomology of Shimura varieties are rather rare. According to this and for Kottwitz-Harris-Taylor type of Shimura varieties, we first associate to…

In this paper we define a family of theories, quasi-theories, motivated by quasi-elliptic cohomology. They can be defined from constant loop spaces. With them, the constructions on certain theories can be made in a neat way, such as those…

Replaces Previous version. Includes comments on poincare duality for twisted equivariant in the context of proper and discrete actions and the Baum-Connes Conjecture. We use a spectral sequence proposed by C. Dwyer and previous work by…

Given a henselian pair $(R, I)$ of commutative rings, we show that the relative $K$-theory and relative topological cyclic homology with finite coefficients are identified via the cyclotomic trace $K \to \mathrm{TC}$. This yields a…

The article gives the second part of the treatise on Regular Algebraic $K$-theory (Sections V & VI) of the author. Regular algebraic $K$-theory for groups is a homology theory for discrete groups closely connected to (but different from)…

The purpose of this article is to prove that the category of cocommutative Hopf $K$-algebras, over a field $K$ of characteristic zero, is a semi-abelian category. Moreover, we show that this category is action representable, and that it…

We construct twisted $\mathcal{D}$-modules on the projective line $\mathbb{P}^1$ that are equivariant for the action of the diagonal torus subgroup of $SL_2$. In the most interesting case these arise as extensions from local systems on…

We prove several completion theorems for equivariant K-theory and cyclic homology of schemes with group action over a field. One of these shows that for an algebraic space over a field acted upon by a linear algebraic group, the derived…

Actions of algebraic groups on DG categories provide a convenient, unifying framework in some parts of geometric representation theory, especially the representation theory of reductive Lie algebras. We extend this theory to loop groups and…

There are two approaches to projective representation theory of symmetric and alternating groups, which are powerful enough to work for modular representations. One is based on Sergeev duality, which connects projective representation…