Zobrazeno 1 - 10
of 40
pro vyhledávání: '"Rosengarten, Zev"'
Autor:
Rosengarten, Zev
Publikováno v:
Comptes Rendus. Mathématique, Vol 361, Iss G2, Pp 559-564 (2023)
We prove that an algebraic group over a field $k$ is affine precisely when its Picard group is torsion, and show that in this case the Picard group is finite when $k$ is perfect, and the product of a finite group of order prime to $p$ and a $p$-prima
Externí odkaz:
https://doaj.org/article/c930b04ec28c47a9874e245501752fa7
Autor:
Rosengarten, Zev
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 (almost-)representability beyond the proper setting.
Comment: 30 pages
Comment: 30 pages
Externí odkaz:
http://arxiv.org/abs/2404.07040
Autor:
Rosengarten, Zev
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-Jacobi map from the smooth locus C^{sm} into the Jacobian of C does n
Externí odkaz:
http://arxiv.org/abs/2404.02766
For a connected reductive group $G$ over a local or global field $K$, we define a diamond (or power) operation $$(\xi,n)\mapsto \xi^{\Diamond n}\,\colon\, H^1(K,G)\times {\mathbb Z}\to H^1(K,G)$$ of raising to power $n$ in the Galois cohomology point
Externí odkaz:
http://arxiv.org/abs/2403.07659
Let $k$ be a field and let $G$ be an affine $k$-algebraic group. Call a $G$-torsor weakly versal for a class of $k$-schemes $\mathscr{C}$ if it specializes to every $G$-torsor over a scheme in $\mathscr{C}$. A recent result of the first author, Reich
Externí odkaz:
http://arxiv.org/abs/2401.04458
Autor:
Rosengarten, Zev
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 groups). As a consequence, we deduce several structural results about
Externí odkaz:
http://arxiv.org/abs/2307.04649
Autor:
Rosengarten, Zev
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 useful in the study of general wound unipotent groups. As an illustrati
Externí odkaz:
http://arxiv.org/abs/2303.15605
Autor:
Borovoi, Mikhail, Rosengarten, Zev
Let $G$ be a connected reductive group over a number field $F$, and let $S$ be a set (finite or infinite) of places of $F$. We give a necessary and sufficient condition for the surjectivity of the localization map from $H^1(F,G)$ to the "direct sum"
Externí odkaz:
http://arxiv.org/abs/2209.02069
Autor:
Rosengarten, Zev
We prove that an algebraic group over a field $k$is affine precisely when its Picard group is torsion, and show that in this case the Picard group is finite when $k$ is perfect, and the product of a finite group of order prime to $p$ and a $p$-primar
Externí odkaz:
http://arxiv.org/abs/2205.04959
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 group of multiplicative type). We show that a linear algebraic group is qu
Externí odkaz:
http://arxiv.org/abs/2108.05694