On liftable and weakly liftable modules

Let $T$ be a Noetherian ring and $f$ a nonzerodivisor on $T$. We study concrete necessary and sufficient conditions for a module over $R=T/(f)$ to be weakly liftable to $T$, in the sense of Auslander, Ding and Solberg. We focus on cyclic modules and get various positive and negative results on the lifting and weak lifting problems. For a module over $T$ we define the loci for certain properties: liftable, weakly liftable, having finite projective dimension and study their relationships

Remarks on non-commutative crepant resolutions of complete intersections

We study obstructions to existence of non-commutative crepant resolutions, in the sense of Van den Bergh, over local complete intersections

A note on Higgs decays into ZZ boson and J/Ψ(Υ)J/\Psi (\Upsilon)

Rare decays $h\to Z V$ with $V$ denoting the narrow $c\bar{c}$ or $b\bar{b}$ resonances, such as $J/\Psi$ or $\Upsilon$ states, have been analyzed. Within the standard model, these channels may proceed through the tree-level transition $h\to ZZ^*$ with the virtual $Z^*\to V$, and also loop-induced process $h\to Z\gamma^*$, followed by $\gamma^*\to V$. Our analysis shows that, for the bottomonium final states, the decay rate of $h\to Z \Upsilon$ from the loop-induced process is small and the former transition gives the dominant contribution; while, for the charmonium final states, $\Gamma(h\to Z J/\Psi)$ and $\Gamma(h\to Z\Psi(2S))$ induced by $h\to Z\gamma^* \to Z V$ could be comparable to the contribution given by the tree-level $h\to ZZ^*\to Z V$ transition.Comment: 6 pages, 2 figure

Average size of 2-Selmer groups of Jacobians of hyperelliptic curves over function fields

In this paper, we are going to compute the average size of 2-Selmer groups of two families of hyperelliptic curves with marked points over function fields. The result will be obtained by a geometric method which could be considered as a generalization of the one that was used previously by Q.P. Ho, V.B. Le Hung, and B.C. Ngo to obtain the average size of 2-Selmer groups of elliptic curves