In this article, we first investigate the properties of modular Frobenius groups. Then, we consider the case that G＇ is a minimal normal subgroup of a modular Frobenius group G. We give the complete classification of...In this article, we first investigate the properties of modular Frobenius groups. Then, we consider the case that G＇ is a minimal normal subgroup of a modular Frobenius group G. We give the complete classification of G when G＇ as a modular Frobenius kernel has no more than four conjugacy classes in G.展开更多
Let k be an algebraically closed field of characteristic p 〉 0, X a smooth projective variety over k with a fixed ample divisor H, FX：X → X the absolute Frobenius morphism on X. Let E be a rational GLn（k）-bundle ...Let k be an algebraically closed field of characteristic p 〉 0, X a smooth projective variety over k with a fixed ample divisor H, FX：X → X the absolute Frobenius morphism on X. Let E be a rational GLn（k）-bundle on X, and ρ：GLn（k） → GLm（k） a rational GLn（k）-representation of degree at most d such that ρ maps the radical R（GLn（k）） of GLn（k） into the radical R（GLm（k）） of GLm（k）. We show that if FXN＊（E） is semistable for some integer N ≥ max0 〈 r 〈 m （rm） · logp（dr）, then the induced rational GLm（k）-bundle E（GLm（k）） is semistable. As an application, if dim X=n, we get a sufficient condition for the semistability of Frobenius direct image FX＊（ρ＊（ΩX1））, where ρ＊（ΩX1） is the vector bundle obtained from ΩX1 via the rational representation ρ.展开更多
基金Supported by the National Natural Science Foundation of China (11171243, 11201385)the Technology Project of Department of Education of Fujian Province(JA12336)+1 种基金the Fundamental Research Funds for the Central Universities (2010121003)the Science and the Natural Science Foundation of Fujian Province (2011J01022)
文摘In this article, we first investigate the properties of modular Frobenius groups. Then, we consider the case that G＇ is a minimal normal subgroup of a modular Frobenius group G. We give the complete classification of G when G＇ as a modular Frobenius kernel has no more than four conjugacy classes in G.
基金Supported by National Natural Science Foundation of China(Grant No.11501418)Shanghai Sailing Program(Grant No.15YF1412500)
文摘Let k be an algebraically closed field of characteristic p 〉 0, X a smooth projective variety over k with a fixed ample divisor H, FX：X → X the absolute Frobenius morphism on X. Let E be a rational GLn（k）-bundle on X, and ρ：GLn（k） → GLm（k） a rational GLn（k）-representation of degree at most d such that ρ maps the radical R（GLn（k）） of GLn（k） into the radical R（GLm（k）） of GLm（k）. We show that if FXN＊（E） is semistable for some integer N ≥ max0 〈 r 〈 m （rm） · logp（dr）, then the induced rational GLm（k）-bundle E（GLm（k）） is semistable. As an application, if dim X=n, we get a sufficient condition for the semistability of Frobenius direct image FX＊（ρ＊（ΩX1））, where ρ＊（ΩX1） is the vector bundle obtained from ΩX1 via the rational representation ρ.
