Effective bounds for Brauer groups of Kummer surfaces over number fields
We study effective bounds for Brauer groups of Kummer surfaces associated to the Jacobians of curves of genus $2$ defined over number fields.
math.NT↗
arXiv subjects
Yunqing Tang
Publications and source records attributed to Yunqing Tang.
Algebraic solutions of differential equations over the projective line minus three points
The Grothendieck--Katz $p$-curvature conjecture predicts that an arithmetic differential equation whose reduction modulo $p$ has vanishing $p$-curvatures for {\em almost all} $p,$ has finite monodromy. It is known that it suffices to prove the conjecture for differential equations on $\mathbb{P}^{1}-\{0,1,\infty\}.$ We prove a variant of this conjecture for $\mathbb{P}^{1}-\{0,1,\infty\},$ which asserts that if the equation satisfies a certain convergence condition for {\em all} $p,$ then its monodromy is trivial. For those $p$ for which the $p$-curvature makes sense, its vanishing implies our condition. We deduce from this a description of the differential Galois group of the equation in terms of $p$-curvatures and certain local monodromy groups. We also prove similar variants of the $p$-curvature conjecture for the elliptic curve with $j$-invariant $1728$ minus its identity and for $\mathbb{P}^1-\{\pm 1,\pm i,\infty\}$.
math.AG↗
Electric Current Focusing Efficiency in Graphene Electric Lens
In present work, we theoretically study the electron wave's focusing phenomenon in a single layered graphene pn junction(PNJ) and obtain the electric current density distribution of graphene PNJ, which is in good agreement with the qualitative result in previous numerical calculations [Science, 315, 1252 (2007)]. In addition, we find that for symmetric PNJ, 1/4 of total electric current radiated from source electrode can be collected by drain electrode. Furthermore, this ratio reduces to 3/16 in a symmetric graphene npn junction. Our results obtained by present analytical method provide a general design rule for electric lens based on negative refractory index systems.
cond-mat.mes-hall↗