Zobrazeno 1 - 10
of 353
pro vyhledávání: '"20G30"'
Autor:
Luger, Cedric
Let $K$ be a number field, let $X$ be a smooth integral variety over $K$, and assume that there exists a finite set of finite places $S$ of $K$ such that the $S$-integral points on $X$ are dense. Then the combined conjectures of Campana and Corvaja-Z
Externí odkaz:
http://arxiv.org/abs/2410.13403
Autor:
Đonlagić, Azur
Questions related to Brauer-Manin obstructions to the Hasse principle and weak approximation for homogeneous spaces of tori over a number field are well-studied, generally using arithmetic duality theorems, starting with works of Sansuc and of Collio
Externí odkaz:
http://arxiv.org/abs/2410.12127
Autor:
Borovoi, Mikhail
Let $K$ be a local or global field. For a connected reductive group $G$ over $K$, in another preprint [5] we defined a 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
Externí odkaz:
http://arxiv.org/abs/2410.04474
Autor:
Borovoi, Mikhail
Let K be a global field, that is, a number field or a global function field. It is known that the answer to the question in the title over K is "Yes" when K has no real embeddings. We show that otherwise the answer is "No". Namely, we show that when
Externí odkaz:
http://arxiv.org/abs/2408.16783
Autor:
Borovoi, Mikhail
Using ideas and results of Sansuc, Colliot-Th\'el\`ene, and Tate, we compute the defect of weak approximation for a reductive group G over a global field K in terms of the algebraic fundamental group of G.
Comment: v1: 12 pages; v2: 13 pages; v3
Comment: v1: 12 pages; v2: 13 pages; v3
Externí odkaz:
http://arxiv.org/abs/2406.08017
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 $n \geqslant 2$. We prove that, up to conjugation, $\mathrm{Sp}_{2n} (\mathbf{Z})$ is the lattice in $\mathrm{Sp}_{2n} (\mathbf{R})$ which has the smallest covolume.
Comment: 28 pages, comments welcome!
Comment: 28 pages, comments welcome!
Externí odkaz:
http://arxiv.org/abs/2402.07604
Autor:
Mason, A. W., Schweizer, Andreas
Let $A$ be the ring of elements in an algebraic function field $K$ over $\mathbb{F}_q$ which are integral outside a fixed place $\infty$. In contrast to the classical modular group $SL_2(\mathbb{Z})$ and the Bianchi groups, the {\it Drinfeld modular
Externí odkaz:
http://arxiv.org/abs/2401.04604
Autor:
Gelander, Tsachik, Slutsky, Raz
We show that an arithmetic lattice $\Gamma$ in a semi-simple Lie group $G$ contains a torsion-free subgroup of index $\delta(v)$ where $v = \mu (G/\Gamma)$ is the co-volume of the lattice. We prove that $\delta$ is polynomial in general and poly-loga
Externí odkaz:
http://arxiv.org/abs/2311.15976
Autor:
Ivanov, Alexander B., Paladino, Laura
We show that the local-global divisibility in commutative algebraic groups defined over number fields can be tested on sets of primes of arbitrary small density, i.e. stable and persistent sets. We also give a new description of the cohomological gro
Externí odkaz:
http://arxiv.org/abs/2309.03514