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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Vanishing of some algebraic cycles on powers of Shimura curves
志村曲线 幂 代数 循环消失
2023/4/27
For a smooth projective variety over a number field, the Beilinson—Bloch conjecture predicts that Chow groups of algebraic cycles modulo rational equivalence can be determined using cohomological data...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：The algebraic incarnations of the Artin Vanishing
Artin 消失 代数化身
2023/5/16
The non-abelian Hodge theory, briefly can be viewed as building a correspondence between certain topological objects, analytic objects, and algebraic objects. In this talk, I will show that Kodaira-ty...
Algebraic proofs over noncommutative formulas
Proof complexity Algebraic proof systems Frege proofs Lower bounds Polynomial calculus
2012/12/4
We study possible formulations of algebraic propositional proof systems operating with noncommutative formulas. We observe that a simple formulation gives rise to systems at least as strong as Frege, ...
On the degree of a Kloosterman sum as an algebraic integer
cyclotomic field Kloosterman sum
2011/8/22
Abstract: The maximal degree over rational numbers that an n-dimensinonal Kloosterman sum defined over a finite field of characteristic p can achieve is known to be (p-1)/d where d=gcd(p-1,n+1). Wan h...
Algebraic density property of Danilov-Gizatullin surfaces
Algebraic density property Danilov-Gizatullin surfaces
2010/12/9
A Danilov-Gizatullin surface is an affine surface V which is the com-plement of an ample section S of a Hirzebruch surface. The remarkable theorem of Danilov and Gizatullin states that the isomorphism...
A crucial observation in Quillen’s definition of higher algebraic K-theory was
that the right way to proceed is to define the higer K-groups as the homotopy
groups of a space ([21]). Qui...
Cahit Arf's Contribution to Algebraic number Theory and Related Fields
Algebraic number Cahit Arf's Related Fields
2010/3/4
Cahit Arf's Contribution to Algebraic number Theory and Related Fields。