Edward Snowden，前美国国家安全局（NSA）的签约雇员，在2013年上半年亲手把国家安全局的一批秘密文件交给了媒体记者．2013年6月媒体首次发表这些文件，披露了美国国家安全局和其他政府组织——如英国的政府通讯总部（GCHQ）——的大...Edward Snowden，前美国国家安全局（NSA）的签约雇员，在2013年上半年亲手把国家安全局的一批秘密文件交给了媒体记者．2013年6月媒体首次发表这些文件，披露了美国国家安全局和其他政府组织——如英国的政府通讯总部（GCHQ）——的大量秘密监视项目．这些文件的披露引起全世界的反响．它触及到一些大企业的损益底线，牵动着国际社会上层人物的关系，也影响到普通民众与日俱增的使用网络和手机的日常活动．展开更多
This paper establishes an asymptotic formula with a power-saving error term for the number of rational points of bounded height on the singular cubic surface of P3 Qgiven by the following equation x0（x12+ x22）-x33= ...This paper establishes an asymptotic formula with a power-saving error term for the number of rational points of bounded height on the singular cubic surface of P3 Qgiven by the following equation x0（x12+ x22）-x33= 0 in agreement with the Manin-Peyre conjectures.展开更多
Let p be a prime, P a finite p-group and F- a Frobenius P-category. The question on the existence of a suitable category L^scextending the full subcategory of F over the set of F-selfcentralizing subgroups of P goes b...Let p be a prime, P a finite p-group and F- a Frobenius P-category. The question on the existence of a suitable category L^scextending the full subcategory of F over the set of F-selfcentralizing subgroups of P goes back to Dave Benson in 1994. In 2002 Carles Broto, Ran Levi and Bob Oliver formulate the existence and the uniqueness of the category L^sc in terms of the annulation of an obstruction 3-cohomology element and of the vanishing of a 2-cohomology group, and they state a sufficient condition for the vanishing of these n-cohomology groups. Recently, Andrew Chermak has proved the existence and the uniqueness of L^sc via his objective partial groups, and Bob Oliver, following some of Chermak＇s methods, has also proved the vanishing of those n-cohomology groups for n 〉1, both applying the Classification of the finite simple groups. Here we give direct proofs of the existence and the uniqueness of L^sc; moreover, in [11] we already show that L^sc can be completed in a suitable category L extending F and we also prove some functoriality of this correspondence.展开更多
We introduce a new avatar of a Frobenius P-category F under the form of a suitable subring HF of the double Burnside ring of P -- called the Hecke algebra of F- where we are able to formulate： （i） the generalizatio...We introduce a new avatar of a Frobenius P-category F under the form of a suitable subring HF of the double Burnside ring of P -- called the Hecke algebra of F- where we are able to formulate： （i） the generalization to a Frobenius P-category of the Alperin Fusion Theorem, （ii） the ＂canonical decomposition＂ of the morphisms in the exterior quotient of a Frobenius P-category restricted to the selfcentralizing objects as developed in chapter 6 of [4], and （iii） the ＂basic P × P-sets＂ in chapter 21 of [4] with its generalization by Kari Ragnarsson and Radu Stancu to the virtual P ×P-sets in [6]. We also explain the relationship with the usual Hecke algebra of a finite group.展开更多
Let p be a prime,P a finite p-group and F a Frobenius P-category.In[Existcnee,uniqueness and functoriality of the perfect locality over a Frobenius P-category,Algebra Colloq.23(2016)541-622],we claimed the uniqueness ...Let p be a prime,P a finite p-group and F a Frobenius P-category.In[Existcnee,uniqueness and functoriality of the perfect locality over a Frobenius P-category,Algebra Colloq.23(2016)541-622],we claimed the uniqueness of the partial perfect locality over any up-closed set X of J--selfcentralizing subgroups of P,but recently Bob Oliver exhibits some counter-cxamplcs,demanding some revision of our arguments.In this note we show that,up to replacing the perfect localities by the extendable perfect localities over any up-closed set X of J7-selfcentralizing subgroups of P,our arguments are correct,still proving the existence and the uniqueness of the perfect J730-locality,since it is extendable.We take advantage of this revision to simplify some of our arguments.展开更多
基金supported by the program PRC 1457-Au For Di P(CNRS-NSFC)supported by National Natural Science Foundation of China(Grant No.11531008)+1 种基金the Ministry of Education of China(Grant No.IRT16R43)the Taishan Scholar Project of Shandong Province
文摘This paper establishes an asymptotic formula with a power-saving error term for the number of rational points of bounded height on the singular cubic surface of P3 Qgiven by the following equation x0（x12+ x22）-x33= 0 in agreement with the Manin-Peyre conjectures.
文摘Let p be a prime, P a finite p-group and F- a Frobenius P-category. The question on the existence of a suitable category L^scextending the full subcategory of F over the set of F-selfcentralizing subgroups of P goes back to Dave Benson in 1994. In 2002 Carles Broto, Ran Levi and Bob Oliver formulate the existence and the uniqueness of the category L^sc in terms of the annulation of an obstruction 3-cohomology element and of the vanishing of a 2-cohomology group, and they state a sufficient condition for the vanishing of these n-cohomology groups. Recently, Andrew Chermak has proved the existence and the uniqueness of L^sc via his objective partial groups, and Bob Oliver, following some of Chermak＇s methods, has also proved the vanishing of those n-cohomology groups for n 〉1, both applying the Classification of the finite simple groups. Here we give direct proofs of the existence and the uniqueness of L^sc; moreover, in [11] we already show that L^sc can be completed in a suitable category L extending F and we also prove some functoriality of this correspondence.
文摘We introduce a new avatar of a Frobenius P-category F under the form of a suitable subring HF of the double Burnside ring of P -- called the Hecke algebra of F- where we are able to formulate： （i） the generalization to a Frobenius P-category of the Alperin Fusion Theorem, （ii） the ＂canonical decomposition＂ of the morphisms in the exterior quotient of a Frobenius P-category restricted to the selfcentralizing objects as developed in chapter 6 of [4], and （iii） the ＂basic P × P-sets＂ in chapter 21 of [4] with its generalization by Kari Ragnarsson and Radu Stancu to the virtual P ×P-sets in [6]. We also explain the relationship with the usual Hecke algebra of a finite group.
文摘Let p be a prime,P a finite p-group and F a Frobenius P-category.In[Existcnee,uniqueness and functoriality of the perfect locality over a Frobenius P-category,Algebra Colloq.23(2016)541-622],we claimed the uniqueness of the partial perfect locality over any up-closed set X of J--selfcentralizing subgroups of P,but recently Bob Oliver exhibits some counter-cxamplcs,demanding some revision of our arguments.In this note we show that,up to replacing the perfect localities by the extendable perfect localities over any up-closed set X of J7-selfcentralizing subgroups of P,our arguments are correct,still proving the existence and the uniqueness of the perfect J730-locality,since it is extendable.We take advantage of this revision to simplify some of our arguments.
