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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：The Brauer-Manin obstruction on algebraic stacks
代数栈 Brauer-Manin阻塞 Hasse原理
2023/11/29
The Brauer-Manin obstruction is an old topic in local-global principle of varieties. I will talk about Brauer-Manin obstruction on algebraic stacks and extend some classical results such as the exact ...
School Colloquium——Stable reduction of algebraic curves and abelian varieties
北大 algebraic curves abelian varieties
2023/6/16
The stable reduction theorem was proved by Grothendieck for Abelian varieties and subsequently by Deligne and Mumford for projective curves.
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Application of algebraic curve theory to integrable systems
代数曲线理论 可积系统 紧黎曼曲面
2023/5/5
We first consider the basic theory of algebraic curves, including the compact Riemann surface, Riemann-Hurwitz formula, Baker-Akhiezer function, three kinds of Abelian differentials, the construction ...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：On open subgroups of p-adic algebraic groups
p-adic 代数群 开子群
2023/5/5
In this talk, I will breifly introduce the p-aidc number, p-aidc manifolds, p-adic algebraic groups and p-aidc definable groups. Using an elementary method, I will show that every open subgroup of a c...
三亚国际数学论坛：Asymptotic,Algebraic and Geometric Aspects of Integrable Systems
三亚国际数学论坛 Asymptotic Algebraic Geometric Aspects Integrable Systems
2017/11/24
Integrable systems involves the study of physically relevant nonlinear equations, which includes many families of well-known, highly important partial and ordinary differential equations. Building on ...
The 41st International Symposium on Symbolic and Algebraic Computation (ISSAC)
Symbolic Algebraic Computation
2016/7/19
The International Symposium on Symbolic and Algebraic Computation (ISSAC) is the premier conference for research in symbolic computation and computer algebra. ISSAC 2016 will be the 41st meeting in th...
We define an extended Bloch group for an arbitrary field F, and
show that this group is naturally isomorphic to Kind
3
(F) if F is a number
field. This gives an explicit descript...
The de Rham-Witt and Zp-cohomologies of an algebraic variety
algebraic variety Zp-cohomologies
2015/12/10
According to the standard philosophy (cf. Deligne 1994, 3.1), a cohomology theory X 7→
Hi
(X, r) on the algebraic varieties over a fixed field k should arise from a functor RΓ
taking va...
On representation varieties of Artin groups,projective arrangements and the fundamental groups of smooth complex algebraic varieties
Artin groups,projective arrangements fundamental groups smooth complex algebraic varieties
2015/10/14
On representation varieties of Artin groups,projective arrangements and the fundamental groups of smooth complex algebraic varieties.
Essential dimension is a numerical invariant of an algebraic
group G introduced by J. Buhler and the second author to study the
complexity of G-torsors over a eld K. It has since been studied by se...
This paper is the sequel to The radiance obstruction and par-
allel forms on a;ffne manifolds (lYans. Amer. Math. Soc. 286 (1984),
629 649) which introduced a new family of secondary characteristi...
ABELIAN VARIETIES OVER LARGE ALGEBRAIC FIELDS WITH INFINITE TORSION
ABELIAN VARIETIES OVER LARGE ALGEBRAIC FIELDS INFINITE TORSION
2015/8/26
Let A be a non-zero abelian variety defined over a number field K and let K be a fixed algebraic closure of K. For each element σ of the absolute Galois group Gal(K/K), let K(σ) be the fixed field in ...
Derived Representation Theory and the Algebraic K-theory of Fields
Algebraic K-theory of Fields Derived Representation Theory
2015/7/7
Quillen’s higher algebraic K-theory for fields F has been the object of intense
study since their introduction in 1972 [26]. The main direction of research has
been the construction of “descen...
Structured Stable Homotopy Theory and the Descent Problem for the Algebraic K-theory of Fields
Structured Stable Homotopy Theory Algebraic K-theory
2015/7/7
his is a relative result which asserts that the K-theory spectra of any two
algebraically closed fields of a given characteristic are equivalent to each other
after completion at a prime not e...
Let k be a eld, and let G be an algebraic group over k, by which we mean a connected smooth k-group
scheme (not necessarily ane). Recall that such a G is automatically separated, nite type, and ge...