Roy Joshua | Ohio State University (original) (raw)

Papers by Roy Joshua

Designs, Codes and Cryptography, Oct 26, 2023

HAL (Le Centre pour la Communication Scientifique Directe), Nov 1, 2008

Journal of Algebra, 1998

In this paper, we provide a general functorial construction of modules over Ž convolution algebra... more In this paper, we provide a general functorial construction of modules over Ž convolution algebras i.e., where the multiplication is provided by a convolution. operation starting with an appropriate equivariant derived category. The construction is sufficiently general to be applicable to different situations. One of the main applications is to the construction of modules over the graded Hecke algebras associated to complex reductive groups starting with equivariant complexes on the unipotent variety. It also applies to the affine quantum enveloping algebras of type A. As is already known, in each case the algebra can be realized as a convolution n algebra. Our construction turns suitable equi¨ariant deri¨ed categories into an abundant source of modules o¨er such algebras; most of these are new, in that, so far the only modules have been provided by suitable Borel᎐Moore homology or cohomol-Ž. ogy with respect to a constant sheaf or by an appropriate K-theoretic variant. In a sequel to this paper we will apply these constructions to equivariant perverse sheaves and also obtain a general multiplicity formula for the simple modules in the composition series of the modules constructed here.

Duke Mathematical Journal, 1991

In this paper we study the higher K-theory (and thederived category) of weakly equivariant algebr... more In this paper we study the higher K-theory (and thederived category) of weakly equivariant algebraic Y-modules on smooth complex algebraic varieties that are weakly equivariant for theaction of complex linear algebraic groups. We begin by recalling the basic terminology ...

preprint, 2001

AbWtract. In this talk we will explore in detail the strong Kunneth decomposition for the class o... more AbWtract. In this talk we will explore in detail the strong Kunneth decomposition for the class of the diagonal for the product of two schemes. In the first part of the talk I will discuss the strong Kunneth decomposition and its consequences in a general setting. The second ...

Preprint (http://www. math. uiuc. edu/K-theory/0733/), 2005

Abstract. One of the main obstacles for proving Riemann-Roch for algebraic stacks is the lack of ... more Abstract. One of the main obstacles for proving Riemann-Roch for algebraic stacks is the lack of cohomology and homology theories that are closer to the K-theory and G-theory of algebraic stacks than the traditional cohomology and homology theories for algebraic ...

American Journal of Mathematics, 1987

... It is clear that Xi so defined is Co and also G-equivariant. Next let ( 4-2(n+ 1)2 * Gi = ori... more ... It is clear that Xi so defined is Co and also G-equivariant. Next let ( 4-2(n+ 1)2 * Gi = ori, . . .,9ari) Page 11. BECKER-GOTTLIEB TRANSFER 463 (Each Gi is now a Co-function on Ui to (n + 1)R2(n+ ".) Extend Gi to all of U{gUi Ig E G} by defining Gi(gui) = gGi(ui), ui E Ui. ...

Advances in Mathematics, Sep 1, 2023

arXiv (Cornell University), Jun 16, 2023

In this paper, we settle an open conjecture regarding the assertion that the Eulercharacteristic ... more In this paper, we settle an open conjecture regarding the assertion that the Eulercharacteristic of G/NG(T) for a split reductive group scheme G and the normalizer of a split maximal torus NG(T) over a field is 1 in the Grothendieck-Witt ring with the characteristic exponent of the field inverted, under the assumption that the base field contains a √ −1. Numerous applications of this to splittings in the motivic stable homotopy category and to Algebraic K-Theory are worked out in several related papers by Gunnar Carlsson and the authors.

Finite Fields and Their Applications, Dec 1, 2021

Abstract We compute the parameters of the linear codes that are associated with all projective em... more Abstract We compute the parameters of the linear codes that are associated with all projective embeddings of Grassmann varieties.

Finite Fields and Their Applications, Aug 1, 2023

Non UBCUnreviewedAuthor affiliation: Ohio State UniversityFacult

American Journal of Mathematics, 1996

The main result of the paper is that the equivariant intersection cohomology of the semistable po... more The main result of the paper is that the equivariant intersection cohomology of the semistable points on a complex projective variety, for the action of a complex reductive group, may be determined from the equivariant intersection cohomology of the semi-stable points for the action of a maximal torus. It extends the work of Brion who considered the smooth case using equivariant cohomology. Equivariant intersection cohomology is a theory due to Brylinski and the second author. As an application, a surprising relation between the intersection cohomology of Chow hypersurfaces is established in the last section of the paper. 1. We will first recall some basic terminology from [Br] p. 126. Let G denote a complex connected reductive group, with T a chosen maximal torus and W = N G (T)=T its Weyl group. S will denote the symmetric algebra on the group of characters of T tensored with Q and S W will denote the invariants for the action of W on S. We make S into a graded algebra by assigning the degree 2 to the characters of T. H will denote the graded W sub-module of S formed of the elements that are W-harmonic, i.e., killed by every differential operator with constant coefficients, invariant by W and with no constant term. Then H is isomorphic to the regular representation of W and the multiplication of S induces an isomorphism of S W H with S as modules over W and over S W. Let denote the signature of W. For every W-module M, one denotes by M a the set Manuscript received

Preprint, 2006

We describe the equivariant Chow ring of the wonderful compactification X of a symmetric space of... more We describe the equivariant Chow ring of the wonderful compactification X of a symmetric space of minimal rank, via restriction to the associated toric variety Y. Also, we show that the restrictions to Y of the tangent bundle T X and its logarithmic analogue S X decompose into a direct sum of line bundles. This yields closed formulae for the equivariant Chern classes of T X and S X , and, in turn, for the Chern classes of reductive groups considered by Kiritchenko.

Advances in Mathematics, 2007

One of the main obstacles for proving Riemann-Roch for algebraic stacks is the lack of cohomology... more One of the main obstacles for proving Riemann-Roch for algebraic stacks is the lack of cohomology and homology theories that are closer to the K-theory and G-theory of algebraic stacks than the traditional cohomology and homology theories for algebraic stacks. In this paper we study in detail a family of cohomology and homology theories which we call Bredon-style theories that are of this type and in the spirit of the classical Bredon cohomology and homology theories defined for the actions of compact topological groups on topological spaces. We establish Riemann-Roch theorems in this setting: it is shown elsewhere that such Riemann-Roch theorems provide a powerful tool for deriving formulae involving virtual fundamental classes associated to dg-stacks, for example, moduli stacks of stable curves provided with a virtual structure sheaf associated to a perfect obstruction theory. We conclude the present paper with a brief application of this nature.

math.osu.edu

Abstract. Computing intersection cohomology Betti numbers is complicated by the fact that the usu... more Abstract. Computing intersection cohomology Betti numbers is complicated by the fact that the usual long exact localization sequences in Borel-Moore homology do not carry over to the setting of intersection homology. Nevertheless, about 20 years ago, Richard Stanley ...