Categorizations of Limits of Grothendieck Groups over a Frobenius P-Category  

作　　者：Lluis Puig 

机构地区：[1]Carrer de La Cort 16,Vilafranca del Penedes,France

出　　处：《Algebra Colloquium》2022年第4期541-594,共54页代数集刊（英文版）

摘　　要：In[Frobenius Categories Versus Brauer Blocks,Progress in Math.,274]and in[Ordinary Grothendieck groups of a Frobenius P-category,Algebra Colloq.18(2011)1-76],we consider suitable inverse limits of Grothendieck groups of categories of modules in characteristics p and zero,obtained from a folded Frobenius P-category(F,aut_(F)sc),which covers the case of the Frobenius P-categories associated with blocks;moreover,in[Beyond a question of Markus Linckelmann,arxiv.org/abs/1507.04278]we show that a folded Frobenius P-category is actually equivalent to the choice of a regular central k^(*)-extension F^(SC) of F^(SC) c.Here,taking advantage of the existence of a perfect F^(SC) -locality P^(SC) we exhibit those inverse limits as the true Grothendieck groups of the categories of K_(*)G-and k_(*)G-modules for a suitable k_(*)-group G associated to the k^(*)-category P^(SC) obtained from P^(SC) and F^(SC) .It depends on a vanishing cohomology result,given with more generality intheAppendix.

关 键 词：Frobenius category Grothendieckgroup perfect locality 

分 类 号：O15[理学—数学]