Letℓ≥2 be a fixed positive integer and Q(y)be a positive definite quadratic form inℓvariables with integral coefficients.The aim of this paper is to count rational points of bounded height on the cubic hypersurface d...Letℓ≥2 be a fixed positive integer and Q(y)be a positive definite quadratic form inℓvariables with integral coefficients.The aim of this paper is to count rational points of bounded height on the cubic hypersurface defined by u^(3)=Q(y)z.We can get a power-saving result for a class of special quadratic forms and improve on some previous work.展开更多
The Dieudonne Manin classification theorem on φ-modules （φ-isocrystals） over a perfect field plays a very important role in p-adic Hodge theory. In this note, in a more general setting we give a new proof of this ...The Dieudonne Manin classification theorem on φ-modules （φ-isocrystals） over a perfect field plays a very important role in p-adic Hodge theory. In this note, in a more general setting we give a new proof of this result, and in the course of the proof, we also give an explicit construction of the Harder Narasimhan filtration of a φ-module.展开更多
In this paper, we first show that there is a Hom-Lie algebra structure on the set of(σ, σ)-derivations of an associative algebra. Then we construct the dual representation of a representation of a Hom-Lie algebra.We...In this paper, we first show that there is a Hom-Lie algebra structure on the set of(σ, σ)-derivations of an associative algebra. Then we construct the dual representation of a representation of a Hom-Lie algebra.We introduce the notions of a Manin triple for Hom-Lie algebras and a purely Hom-Lie bialgebra. Using the coadjoint representation, we show that there is a one-to-one correspondence between Manin triples for Hom-Lie algebras and purely Hom-Lie bialgebras. Finally, we study coboundary purely Hom-Lie bialgebras and construct solutions of the classical Hom-Yang-Baxter equations in some special Hom-Lie algebras using Hom-O-operators.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
A construction of A-adic modular forms from p-adic modular symbols is described. It shows that each A linear map satisfying some certain conditions from the module of p-adic modular symbols to A corresponds to a A-adi...A construction of A-adic modular forms from p-adic modular symbols is described. It shows that each A linear map satisfying some certain conditions from the module of p-adic modular symbols to A corresponds to a A-adic modular form.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.11971476).
文摘Letℓ≥2 be a fixed positive integer and Q(y)be a positive definite quadratic form inℓvariables with integral coefficients.The aim of this paper is to count rational points of bounded height on the cubic hypersurface defined by u^(3)=Q(y)z.We can get a power-saving result for a class of special quadratic forms and improve on some previous work.
基金Partially supported by National Natural Science Foundation of China(Grant No.10871183)Partially supported by Specialized Research Fund for the Doctoral Program of Higher Education(Grant No.200803580047)Partially supported by the Fundamental Research Funds for the Central Universities(Grant No.0010000006)
文摘The Dieudonne Manin classification theorem on φ-modules （φ-isocrystals） over a perfect field plays a very important role in p-adic Hodge theory. In this note, in a more general setting we give a new proof of this result, and in the course of the proof, we also give an explicit construction of the Harder Narasimhan filtration of a φ-module.
基金Natural Science Foundation of Gansu Province(22JR11RA138,20JR5RA249)National Natural Science Foundation of China(12071191)Funds for Innovative Fundamental Research Group Project of Gansu Province(23JRRA684)。
基金supported by National Natural Science Foundation of China (Grant No. 11471139)Natural Science Foundation of Jilin Province (Grant No. 20170101050JC)Nan Hu Scholar Development Program of Xin Yang Normal University
文摘In this paper, we first show that there is a Hom-Lie algebra structure on the set of(σ, σ)-derivations of an associative algebra. Then we construct the dual representation of a representation of a Hom-Lie algebra.We introduce the notions of a Manin triple for Hom-Lie algebras and a purely Hom-Lie bialgebra. Using the coadjoint representation, we show that there is a one-to-one correspondence between Manin triples for Hom-Lie algebras and purely Hom-Lie bialgebras. Finally, we study coboundary purely Hom-Lie bialgebras and construct solutions of the classical Hom-Yang-Baxter equations in some special Hom-Lie algebras using Hom-O-operators.
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.
基金Supported by the Natural Science Foundation of Peking University
文摘A construction of A-adic modular forms from p-adic modular symbols is described. It shows that each A linear map satisfying some certain conditions from the module of p-adic modular symbols to A corresponds to a A-adic modular form.
