5 citations · 10 across the 17 of their papers we have counts for
19 papers
Splitting p-primary cohomology classes of tori in characteristic p
Zev Rosengarten
We prove that -primary cohomology classes of a torus over a global function field of characteristic may be split by suitable separable -primary extensions. More preci…
Extensions Of Unirational Groups
Zev Rosengarten
We undertake a study of extensions of unirational algebraic groups. We prove that extensions of unirational groups are also unirational over fields of degree of imperfection , b…
Extensions of Abelian Schemes and the Additive Group
Gabriel Ribeiro, Zev Rosengarten
We compute extension sheaves of abelian schemes and of the additive group by the multiplicative group in the fppf topology. Our main results include a generalized and streamlined p…
The Restricted Picard Functor
Zev Rosengarten
We prove in significant generality the (almost-)representability of the Picard functor when restricted to smooth test schemes. The novelty lies in the fact that we prove such (almo…
(Non-)Extendability of Abel-Jacobi Maps
Zev Rosengarten
We investigate the "natural" locus of definition of Abel-Jacobi maps. In particular, we show that, for a proper, geometrically reduced curve C -- not necessarily smooth -- the Abel…
Algebraic Groups with Torsors That Are Versal for All Affine Varieties
Uriya A. First, Mathieu Florence, Zev Rosengarten
Let be a field and let be an affine algebraic group over . Call a -torsor weakly versal for a class of -schemes if it specializes to every -torsor over…
Rigidity And Unirational Groups
Zev Rosengarten
We prove a rigidity theorem for morphisms from products of open subschemes of the projective line into solvable groups not containing a copy of $\Ga$ (for example, wound unipotent…
Permawound Unipotent Groups
Zev Rosengarten
We introduce the class of permawound unipotent groups, and show that they simultaneously satisfy certain "ubiquity" and "rigidity" properties that in combination render them very u…
Criterion for surjectivity of localization in Galois cohomology of a reductive group over a number field
Mikhail Borovoi, Zev Rosengarten
Let be a connected reductive group over a number field , and let be a set (finite or infinite) of places of . We give a necessary and sufficient condition for the sur…
Picard Groups Of Algebraic Groups And An Affineness Criterion
Zev Rosengarten
We prove that an algebraic group over a field is affine precisely when its Picard group is torsion, and show that in this case the Picard group is finite when is perfect, an…
Quasi-connected reductive groups
Mikhail Borovoi, Andrei A. Gornitskii, Zev Rosengarten
We introduce the notion of a quasi-connected reductive group over an arbitrary field to be an almost direct product of a connected semisimple group and a quasi-torus (a smooth grou…
Moduli Spaces of Morphisms Into Solvable Algebraic Groups
Zev Rosengarten
We construct (in significant generality) moduli spaces representing the functor of morphisms from a scheme into a solvable algebraic group.
Galois cohomology of real quasi-connected reductive groups
Mikhail Borovoi, Andrei A. Gornitskii, Zev Rosengarten
By a quasi-connected reductive group (a term of Labesse) over an arbitrary field we mean an almost direct product of a connected semisimple group and a quasi-torus (a smooth group…
Pathological Behavior of Arithmetic Invariants of Unipotent Groups
Zev Rosengarten
We show that all of the nice behavior for Tamagawa numbers, Tate-Shafarevich sets, and other arithmetic invariants of pseudo-reductive groups over global function fields proved in…
Tamagawa Numbers and Other Invariants of Pseudo-reductive Groups Over Global Function Fields
Zev Rosengarten
We study Tamagawa numbers and other invariants (especially Tate-Shafarevich sets) attached to commutative and pseudo-reductive groups over global function fields. In particular, we…
Translation-Invariant Line Bundles On Linear Algebraic Groups
Zev Rosengarten
We study the Picard groups of connected linear algebraic groups, and especially the subgroup of translation-invariant line bundles. We prove that this subgroup is finite over every…
Tate Duality In Positive Dimension Over Function Fields
Zev Rosengarten
We extend the classical duality results of Poitou and Tate for finite discrete Galois modules over local and global fields (local duality, nine-term exact sequence, etc.) to all af…
An Erdos-Turan Inequality For Compact Simply-Connected Semisimple Lie Groups
Zev Rosengarten
The classical Erd{\" o}s-Turan Inequality bounds how far a sequence of points in the circle is from being equidistributed in terms of its exponential moments. We prove an analogous…
Transitivity of Infinite-Dimensional Extensions of Anosov Diffeomorphisms
Zev Rosengarten, Asaf Reich
We consider extensions of Anosov diffeomorphisms of an infranilmanifold by the real vector space R^ω. Our main result, based on the analogous theorem in finite dimensions proven by…