Colocalising subcategories of modules over finite group schemes

The Hom closed colocalising subcategories of the stable module category of a finite group scheme are classified. This complements the classification of the tensor closed localising subcategories in our previous work. Both classifications involve pi-points in the sense of Friedlander and Pevtsova. We identify for each pi-point an endofinite module which both generates the corresponding minimal localising subcategory and cogenerates the corresponding minimal colocalising subcategory.

[1]  H. Krause,et al.  Stratification for module categories of finite group schemes , 2015, 1510.06773.

[2]  H. Krause,et al.  Stratification and $$\pi $$π-cosupport: finite groups , 2015, 1505.06628.

[3]  K. Yamagata,et al.  Frobenius Algebras I: Basic Representation Theory , 2011 .

[4]  H. Krause,et al.  Stratifying triangulated categories , 2009, 0910.0642.

[5]  A. Neeman.  Colocalizing subcategories of D(R) , 2011 .

[6]  H. Krause,et al.  Colocalizing subcategories and cosupport , 2010, 1008.3701.

[7]  H. Krause,et al.  Local cohomology and support for triangulated categories , 2007, math/0702610.

[8]  A. Suslin.  Detection theorem for finite group schemes , 2006 .

[9]  Julia Collins,et al.  HOMOLOGICAL ALGEBRA , 2021, Lie Groups, Lie Algebras, and Cohomology. (MN-34), Volume 34.

[10]  E. Friedlander,et al.  Π-SUPPORTS FOR MODULES FOR FINITE GROUP SCHEMES , 2006 .

[11]  J. Pevtsova,et al.  Representation-theoretic support spaces for finite group schemes , 2005 .

[12]  Takayoshi Wakamatsu.  On Frobenius algebras , 2003 .

[13]  H. Krause.  A short proof for Auslander’s defect formula , 2003 .

[14]  H. Krause,et al.  Pure injectives and the spectrum of the cohomology ring of a finite group , 2002 .

[15]  A. Suslin,et al.  Support varieties for infinitesimal group schemes , 1997 .

[16]  J. Carlson.  Modules and Group Algebras , 1996 .

[17]  J. Carlson.  Modules and Algebras , 1996 .

[18]  Amnon Neeman,et al.  The Grothendieck duality theorem via Bousfield’s techniques and Brown representability , 1996 .

[19]  W. Crawley-Boevey.  Representations of Algebras and Related Topics: Modules of finite length over their endomorphism rings , 1992 .

[20]  A. Neeman.  The connection between the K-theory localization theorem of Thomason, Trobaugh and Yao and the smashing subcategories of Bousfield and Ravenel , 1992 .

[21]  W. Crawley-Boevey.  Tame Algebras and Generic Modules , 1991 .

[22]  A. Schofield.  TRIANGULATED CATEGORIES IN THE REPRESENTATION THEORY OF FINITE DIMENSIONAL ALGEBRAS (London Mathematical Society Lecture Note Series 119) , 1990 .

[23]  Dieter Happel,et al.  Triangulated categories in the representation theory of finite dimensional algebras , 1988 .

[24]  J. Carlson.  The varieties and the cohomology ring of a module , 1983 .

[25]  W. Waterhouse,et al.  Introduction to Affine Group Schemes , 1979 .

[26]  Melvin Hochster,et al.  Prime ideal structure in commutative rings , 1969 .

[27]  E. Brown.  ABSTRACT HOMOTOPY THEORY , 1965 .

[28]  Robert Steinberg,et al.  Representations of Algebraic Groups , 1963, Nagoya Mathematical Journal.

[29]  E Cline At Worcester,et al.  Journal Fur Die Reine Und Angewandte Mathematik Finite Dimensional Algebras and Highest Weight Categories ') , 2022 .