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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 ...
The stable reduction theorem was proved by Grothendieck for Abelian varieties and subsequently by Deligne and Mumford for projective curves.
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 ...
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...
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 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...
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.
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...
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 ...
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...
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...

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