Reciprocity laws for representations of finite groups (2009)
Chebolu, Sunil K., Minac, Jan, Reis, Clive
Much has been written on reciprocity laws in number theory and their connections with group representations. In this paper we explore more on these connections. We prove a "reciprocity Law" for...
Quotients of absolute Galois groups which determine the entire Galois cohomology (2009)
Chebolu, Sunil K., Efrat, Ido, Mináč, Ján
For prime power $q=p^d$ and a field $F$ containing a root of unity of order $q$ we show that the Galois cohomology ring $H^*(G_F,\dbZ/q)$ is determined by a quotient $G_F^{[3]}$ of the absolute...
Freyd's generating hypothesis with almost split sequences (2008)
Carlson, Jon F., Chebolu, Sunil K., Minac, Jan
Freyd's generating hypothesis for the stable module category of a non-trivial finite group G is the statement that a map between finitely generated kG-modules that belongs to the thick subcategory...
Finite generation of Tate cohomology (2008)
Carlson, Jon F., Chebolu, Sunil K., Minac, Jan
Let G be a finite group and let k be a field of characteristic p. Given a finitely generated indecomposable non-projective kG-module M, we conjecture that if the Tate cohomology $\HHHH^*(G, M)$ of G...
THE GENERATING HYPOTHESIS FOR THE STABLE MODULE CATEGORY (2008)
David J. Benson, Sunil K. Chebolu, J. Daniel Christensen, Ján Mináč
of a finite p-group G, is the statement that a map between finite-dimensional kG-modules factors through a projective if the induced map on Tate cohomology is trivial. We show that Freyd’s...
THE GENERATING HYPOTHESIS FOR THE STABLE MODULE CATEGORY (2008)
David J. Benson, Sunil K. Chebolu, J. Daniel Christensen, Ján Mináč
of a finite p-group G, is the statement that a map between finite-dimensional kG-modules factors through a projective if the induced map on Tate cohomology is trivial. We show that Freyd’s...
Freyd's generating hypothesis for groups with periodic cohomology (2007)
Chebolu, Sunil K., Christensen, J. Daniel, Mináč, Ján
Let $G$ be a finite group and let $k$ be a field whose characteristic $p$ divides the order of $G$. Freyd's generating hypothesis for the stable module category of $G$ is the statement that a map...
The generating hypothesis for the stable module category of a $p$-group (2006)
Benson, David J., Chebolu, Sunil K., Christensen, J. Daniel, Minac, Jan
Freyd's generating hypothesis, interpreted in the stable module category of a finite p-group G, is the statement that a map between finite-dimensional kG-modules factors through a projective if the...
Groups which do not admit ghosts (2006)
Chebolu, Sunil K., Christensen, J. Daniel, Minac, Jan
A ghost in the stable module category of a group G is a map between representations of G that is invisible to Tate cohomology. We show that the only non-trivial finite p-groups whose stable module...
Ghosts in modular representation theory (2006)
Chebolu, Sunil K., Christensen, J. Daniel, Minac, Jan
Let $G$ be a finite $p$-group and let $k$ be a field of characteristic $p$. Recall that the \emph{stable module category} $\StMod(kG)$ is the following tensor triangulated category. The objects are...
We study the triangulated subcategories of compact objects in stable homotopy categories such as the homotopy category of spectra, the derived categories of rings, and the stable module categories of...
Classifying subcategories of modules over a PID (2006)
Let $R$ be a commutative ring. A full additive subcategory $\C$ of $R$-modules is triangulated if whenever two terms of a short exact sequence belong to $\C$, then so does the third term. In this...
Thick subcategories in stable homotopy theory (2006)
In these lectures we give an exposition of the seminal work of Devinatz, Hopkins and Smith which is surrounding the classification of the thick subcategories of finite spectra in stable homotopy...
Refining thick subcategory theorems (2005)
We use a $K$-theory recipe of Thomason to obtain classifications of triangulated subcategories via refining some standard thick subcategory theorems. We apply this recipe to the full subcategories of...
Abelian subcategories closed under extensions: K-theory and decompositions (2005)
A full subcategory of modules over a commutative ring $R$ is wide if it is abelian and closed under extensions. Hovey \cite{wide} gave a classification of wide subcategories of finitely presented...
Krull-Schmidt decompositions for thick subcategories (2005)
Following Krause \cite{Kr}, we prove Krull-Schmidt type decomposition theorems for thick subcategories of various triangulated categories including the derived categories of rings, Noetherian stable...