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Local-global questions for divisibility in commutative algebraic groups
This is a survey focusing on the Hasse principle for divisibility of points in commutative algebraic groups and its relation with the Hasse principle...
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ALMOST CYCLIC REGULAR SEMISIMPLE ELEMENTS IN IRREDUCIBLE REPRESENTATIONS OF SIMPLE ALGEBRAIC GROUPS
Let G be a simple linear algebraic group defined over an algebraically closed field of characteristic p ≥ 0 and let ϕ be a nontrivial p -restricted...
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Algebraic structure and characteristic ideals of fine Mordell–Weil groups and plus/minus Mordell–Weil groups
Given an elliptic curve defined over a number field F , we study the algebraic structure and prove a control theorem for Wuthrich’s fine Mordell–Weil...
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On Chevalley Restriction Theorem for Semi-reductive Algebraic Groups and Its Applications
An algebraic group is called semi-reductive if it is a semi-direct product of a reductive subgroup and the unipotent radical. Such a semi-reductive...
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On when the union of two algebraic sets is algebraic
In universal algebraic geometry, an algebra is called an equational domain if the union of two algebraic sets is algebraic. We characterize...
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Bernoullicity of lopsided principal algebraic actions
We show that the principal algebraic actions of countably infinite groups associated to lopsided elements in the integral group ring satisfying some...
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Algebraic overshear density property
We introduce the notion of the algebraic overshear density property which implies both the algebraic notion of flexibility and the holomorphic notion...
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Algebraic Surgery
The main purpose of this chapter is to introduce a chain complex version of the L-groups and of the surgery obstructions and to identify them with...
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Algebraic Preliminaries
For the sake of reading, here we collect some useful algebraic results, some of them can be found in the monograph [40].
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Intrinsic Ergodicity, Generators, and Symbolic Representations of Algebraic Group Actions
AbstractWe construct natural symbolic representations of intrinsically ergodic, but not necessarily expansive, principal algebraic actions of...
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Existence of moduli spaces for algebraic stacks
We provide necessary and sufficient conditions for when an algebraic stack admits a good moduli space and prove a semistable reduction theorem for...
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Almost-simple affine difference algebraic groups
Affine difference algebraic groups are a generalization of affine algebraic groups obtained by replacing algebraic equations with algebraic...
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Coxeter Groups, Artin Groups, Buildings
The basic notion in this chapter is a Coxeter system...
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Computing the Homology Functor on Semi-algebraic Maps and Diagrams
Develo** an algorithm for computing the Betti numbers of semi-algebraic sets with singly exponential complexity has been a holy grail in...
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Sullivan’s Juvenilia: Surgery and Algebraic Topology
Dennis Sullivan’s early work, despite being strongly motivated by geometric problems, had a strong algebraic nature, certainly much more so than his...
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TOPOLOGICAL NOETHERIANITY FOR ALGEBRAIC REPRESENTATIONS OF INFINITE RANK CLASSICAL GROUPS
Draisma recently proved that polynomial representations of GL ∞ are topologically noetherian. We generalize this result to algebraic representations...
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The Convergences of Part of Algebraic Representatives
Both Adams spectral sequence and Adams–Novikov spectral sequence converge to the stable homotopy groups of sphere π * ( S ). Suppose an element x in the E