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Let $X$ be a smooth projective integral variety over a finitely generated field $k$ of characteristic $p>0$. We show that the finiteness of the exponent of the $p$-primary part of $\mathrm{Br}(X_{k^s})^{G_k}$ is equivalent to the Tate conjecture for
Externí odkaz:
http://arxiv.org/abs/2406.19518
Autor:
Qin, Yanshuai
Let $K$ be a number field, and let $\mathcal{X}$ be a proper regular flat scheme over $\mathcal{O}_{K}$ with a generic fiber $X$ geometrically connected over $K$. We prove that there is an exact sequence up to finite groups $0\rightarrow Sha(Pic_{X/K
Externí odkaz:
http://arxiv.org/abs/2103.06910
Autor:
Qin, Yanshuai
In this article, we prove a $p$-adic analogue of the local invariant cycle theorem for $H^2$ in mixed characteristics. As a result, for a smooth projective variety $X$ over a $p$-adic local field $K$ with a proper flat regular model $\mathcal{X}$ ove
Externí odkaz:
http://arxiv.org/abs/2103.04945
Autor:
Qin, Yanshuai
Let $X$ be a smooth projective variety over a finitely generated field $K$ of characteristic $p>0$. We proved that the finiteness of the $\ell$-primary part of $\mathrm{Br}(X_{K^s})^{G_K}$ for a single prime $\ell\neq p$ will imply the finiteness of
Externí odkaz:
http://arxiv.org/abs/2012.01681
For an abelian variety $A$ over a finitely generated field $K$ of characteristic $p > 0$, we prove that the algebraic rank of $A$ is at most a suitably defined analytic rank. Moreover, we prove that equality, i.e., the BSD rank conjecture, holds for
Externí odkaz:
http://arxiv.org/abs/2012.01337
Autor:
Qin, Yanshuai
Publikováno v:
Math. Z. 307, 18 (2024)
Let $\mathcal{X}\rightarrow C$ be a dominant morphism between smooth irreducible varieties over a finitely generated field $k$ such that the generic fiber $X$ is smooth, projective and geometrically connected. Assuming that $C$ is a curve with functi
Externí odkaz:
http://arxiv.org/abs/2012.01324
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Publikováno v:
In International Journal of Pressure Vessels and Piping February 2021 189
Autor:
Qin, Yanshuai
In this paper, we study the relation between different versions of Tate conjectures for smooth projective varieties over arbitrary finitely generated fields of positive characteristic, generalizing a theorem of Tate for smooth projective varieties ov
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a46b16732cd632d90167c5253bb0898c