arXiv subjects

Zhaorong Jin

Publications and source records attributed to Zhaorong Jin.

3 recordsLinked to original sources

arXiv2024

Hirzebruch-Zagier classes and rational elliptic curves over quintic fields

Conditionally on a conjecture on the étale cohomology of Hilbert modular surfaces and some minor technical assumptions, we establish new instances of the equivariant BSD-conjecture in rank $0$ with applications to the arithmetic of rational elliptic curves over quintic fields. The key ingredients are a refinement of twisted triple product $p$-adic $L$-functions, the construction of a compatible collection of Hirzebruch-Zagier cycles and an explicit reciprocity law relating the two.

math.NT↗

arXiv2020

Euler Systems for $\mathrm{GSp}_4 \times \mathrm{GL}_2$

For a non-endoscopic cohomological cuspidal automorphic representation of $\mathrm{GSp}_4 \times \mathrm{GL}_2$, assumed to be $p$-ordinary, we construct an Euler system for the Galois representation associated to it. Both the construction and the verification of tame norm relations are based on Novodvorsky's integral formula for the $L$-function of $\mathrm{GSp}_4 \times \mathrm{GL}_2$.

math.NT↗

arXiv2013

Endomotives of toric varieties

We construct endomotives associated to toric varieties, in terms of the decomposition of a toric variety into torus orbits and the action of a semigroup of toric morphisms. We show that the endomotives can be endowed with time evolutions and we discuss the resulting quantum statistical mechanical systems. We show that, in particular, one can construct a time evolution related to the logarithmic height function. We discuss relations to F1-geometry.

math-ph↗