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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...
Consider an absolutely simple abelian variety A defined over a number field K. For most places v of K, we study how the reduction Av of A modulo v splits up to isogeny. Assumingthe Mumford–Tate conjec...
On the Commuting variety of a reductive Lie algebra and other related varieties
polynomial algebra complex commuting variety desingularization Gorenstein Cohen-Macaulay rational singularities cohomology
2012/4/18
In this note, one discusses about some varieties which are constructed analogously to the isospectral commuting varieties. These varieties are subvarieties of varieties having very simple desingulariz...
Cohomology of Line Bundles on the Flag Variety for Type G_2
Cohomology of Line Bundles the Flag Variety Quantum Algebra
2011/9/9
Abstract: In the case of an almost simple algebraic group $G$ of type $G_2$ over a field of characteristic $p>0$ we study the cohomology modules of line bundles on the flag variety for $G$. Our main r...
An improvement upon unmixed decomposition of an algebraic variety
unmixed decomposition weakly non-degenerate conditions
2011/1/18
Decomposing an algebraic variety into irreducible or equidimensional components is a fundamental task in classical algebraic geometry and has various applications in modern geometry engineering. Sever...
On the $p$-adic closure of a subgroup of rational points on an Abelian variety
$p$-adic closure subgroup of rational points Abelian variety
2011/2/24
In 2007, B. Poonen (unpublished) studied the p{adic closure of a subgroup of rational points on a commutative algebraic group. More recently, J. Bellache asked the same question for the special case...
Definability of the variety generated by a commutative monoid in the lattice of commutative semigroup varieties
commutative monoid lattice commutative semigroup varieties
2010/11/11
Let M be a commutative monoid. We provide an explicit first-order formular that defines the variety generated by M in the lattice of commutative semigroup varieties.
Irregular locus of the commuting variety of reductive symmetric Lie algebras and rigid pairs
Irregular locus of the commuting variety reductive symmetric Lie algebras and rigid pairs
2010/11/29
The aim of this paper is to describe the irregular locus of the commuting variety of a reductive symmetric Lie algebra. More precisely, we want to enlighten a remark of Popov. In [Po], the irregular l...
摘要 By defining a concept of normal chains, an algorithm to decompose algebraicvarieties is presented, and the applications of this algorithm in solving polynomial equationsand primary decomposition of...