Supported by National Key R&D Program of China(Grant No.2020YFA0713300);NSFC(Grant Nos.11771303,12171327,11911530092,11871045)。
In the spirit of Morse homology initiated by Witten and Floer,we construct two∞-categories A and B.The weak one A comes out of the Morse-Smale pairs and their higher homotopies,and the strict one B concerns the chain...
Supported by NSFC(Grant Nos.12171230,12271249);NSF of Jiangsu Province of China(Grant No.BK20211358)。
It is well known that the concept of cotilting modules generalizes injective cogenerators and in turn,the concept of cosilting modules generalizes cotilting modules.In this paper,we further investigate the close conne...
In this research, we explore the properties and applications of the mapping cone and its variant, the pinched mapping cone. The mapping cone is a construction that arises naturally in algebraic topology and is used to...
supported by National Natural Science Foundation of China(Grant Nos.21022107 and 11771229)。
Sheaves on non-reduced curves can appear in moduli spaces of 1-dimensional semistable sheaves over a surface and moduli spaces of Higgs bundles as well.We estimate the dimension of the stack M_(X)(nC,χ)of pure sheave...
Supported by the National Natural Science Foundation of China(Nos.11661014,11701499,11871063,and 11711530703);the Research Innovation Program Project of Academic Degree Graduate Students in Jiangsu(XKYCX17_029);the Excellent Doctoral Dissertation Foundation Project of Yangzhou University in 2018.
Let H3 be the 9-dimensional Taft Hopf algebra,let r(H3)be the corresponding Green ring of H3,and let Aut(R(H3))be the automorphism group of Green algebra R(H3)=R■Zr(H3)over the real number fieldR.We prove that the qu...
Supported by the National Natural Science Foundation of China(Grant No.11771129).
Let Z>be a principal ideal domain(PID)and M be a module over D.We prove the following two dual results:(i)If M is finitely generated and rr,y are two elements in M such that M/Dx≌M/Dy,then there exists an auto morphi...
Let R be a prime ring of characteristic different from 2, Z(R) its center, L a Lie ideal of R, and m, n, s, t≥> 1 fixed integers with t ≤ m + n + s. Suppose that a is a non-trivial automorphism of R and let φ(x,y)=...
Despite efforts in prevention and intensive care, trauma and subsequent sepsis are still associated with a high mortality rate. Traumatic injury remains the main cause of death in people younger than 45 years and is t...
Multivariate Public Key Cryptography (MPKC) has intensively and rapidly developed during the past three decades. MPKC is a promising candidate for post-quantum cryptography. However, designing it is universally rega...
Supported by National Natural Science Foundation of China(Grant No.11501418);Shanghai Sailing Program(Grant No.15YF1412500)
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 ...