Let k be the algebraic closure of a finite field $\mathbb{F}_q $ and A be a finite dimensional k-algebra with a Frobenius morphism F. In the present paper we establish a relation between the stable module category of ...Let k be the algebraic closure of a finite field $\mathbb{F}_q $ and A be a finite dimensional k-algebra with a Frobenius morphism F. In the present paper we establish a relation between the stable module category of the repetitive algebra ? of A and that of the repetitive algebra of the fixed-point algebra A F. As an application, it is shown that the derived category of A F is equivalent to the subcategory of F-stable objects in the derived category of A when A has a finite global dimension.展开更多
Let X be a smooth projective curve of genus g 2 over an algebraically closed field k of characteristic p>0,and F:X→X(1)the relative Frobenius morphism.Let M s X(r,d)(resp.M ss X(r,d))be the moduli space of(resp.se...Let X be a smooth projective curve of genus g 2 over an algebraically closed field k of characteristic p>0,and F:X→X(1)the relative Frobenius morphism.Let M s X(r,d)(resp.M ss X(r,d))be the moduli space of(resp.semi-)stable vector bundles of rank r and degree d on X.We show that the set-theoretic map S ss Frob:M ss X(r,d)→M ss X(1)(rp,d+r(p-1)(g-1))induced by[E]→[F(E)]is a proper morphism.Moreover,the induced morphism S s Frob:M s X(r,d)→M s X(1)(rp,d+r(p-1)(g-1))is a closed immersion.As an application,we obtain that the locus of moduli space M s X(1)(p,d)consisting of stable vector bundles whose Frobenius pull backs have maximal Harder-Narasimhan polygons is isomorphic to the Jacobian variety Jac X of X.展开更多
Let Q be a quiver with automorphism σ. We prove that semistable representations of Q over F_q give rise to semistable modules over the F_q-algebra A(Q, σ; q) associated with(Q, σ). As an application, we obtain a de...Let Q be a quiver with automorphism σ. We prove that semistable representations of Q over F_q give rise to semistable modules over the F_q-algebra A(Q, σ; q) associated with(Q, σ). As an application, we obtain a description of the semistable subcategories of A(Q, σ; q)-modules and determine the slopes of semistable A(Q, σ; q)-modules in the case that Q is a Dynkin or tame quiver.展开更多
Let Y be a smooth projective surface defined over an algebraically closed field k with char k ≠ 2, and let π ： X → Y be a double covering branched along a smooth divisor. We show that Jx is stable with respect to...Let Y be a smooth projective surface defined over an algebraically closed field k with char k ≠ 2, and let π ： X → Y be a double covering branched along a smooth divisor. We show that Jx is stable with respect to π＊H if the tangent bundle Jy is semi-stable with respect to some ample line bundle H on Y.展开更多
基金the National Natural Science Foundation of China (Grant No.10671016)the 985 Project of Beijing Normal University
文摘Let k be the algebraic closure of a finite field $\mathbb{F}_q $ and A be a finite dimensional k-algebra with a Frobenius morphism F. In the present paper we establish a relation between the stable module category of the repetitive algebra ? of A and that of the repetitive algebra of the fixed-point algebra A F. As an application, it is shown that the derived category of A F is equivalent to the subcategory of F-stable objects in the derived category of A when A has a finite global dimension.
基金supported by National Natural Science Foundation of China (Grant No. 11271275)
文摘Let X be a smooth projective curve of genus g 2 over an algebraically closed field k of characteristic p>0,and F:X→X(1)the relative Frobenius morphism.Let M s X(r,d)(resp.M ss X(r,d))be the moduli space of(resp.semi-)stable vector bundles of rank r and degree d on X.We show that the set-theoretic map S ss Frob:M ss X(r,d)→M ss X(1)(rp,d+r(p-1)(g-1))induced by[E]→[F(E)]is a proper morphism.Moreover,the induced morphism S s Frob:M s X(r,d)→M s X(1)(rp,d+r(p-1)(g-1))is a closed immersion.As an application,we obtain that the locus of moduli space M s X(1)(p,d)consisting of stable vector bundles whose Frobenius pull backs have maximal Harder-Narasimhan polygons is isomorphic to the Jacobian variety Jac X of X.
基金supported by National Natural Science Foundation of China(Grant No.11271043)
文摘Let Q be a quiver with automorphism σ. We prove that semistable representations of Q over F_q give rise to semistable modules over the F_q-algebra A(Q, σ; q) associated with(Q, σ). As an application, we obtain a description of the semistable subcategories of A(Q, σ; q)-modules and determine the slopes of semistable A(Q, σ; q)-modules in the case that Q is a Dynkin or tame quiver.
文摘Let Y be a smooth projective surface defined over an algebraically closed field k with char k ≠ 2, and let π ： X → Y be a double covering branched along a smooth divisor. We show that Jx is stable with respect to π＊H if the tangent bundle Jy is semi-stable with respect to some ample line bundle H on Y.
