arXiv subjects

Chan-Ho Kim

Publications and source records attributed to Chan-Ho Kim.

23 records · Page 2Linked to original sources

arXiv2019

Remarks on Kato's Euler systems for elliptic curves with additive reduction

Extending the former work for the good reduction case, we provide a numerical criterion to verify a large portion of the "Iwasawa main conjecture without $p$-adic $L$-functions" for elliptic curves with additive reduction at an odd prime $p$ over the cyclotomic $\mathbb{Z}_p$-extension. We also deduce the corresponding $p$-part of the Birch and Swinnerton-Dyer formula for elliptic curves of rank zero from the same numerical criterion. We give explicit examples at the end and specify our choice of Kato's Euler system in the appendix.

math.NT↗

arXiv2018

An anticyclotomic Mazur-Tate conjecture for modular forms

Under certain assumptions, we prove an anticyclotomic analogue of the "weak main conjecture" à la Mazur and Tate for modular forms over a large class of cyclic ring class extensions.

math.NT↗

arXiv2018

Indivisibility of Heegner points and arithmetic applications

We upgrade Howard's divisibility towards Perrin-Riou's Heegner point main conjecture to the predicted equality. Contrary to previous works in this direction, our main result allows for the classical Heegner hypothesis and non-squarefree conductors. The main ingredients we exploit are W.~Zhang's proof of Kolyvagin's conjecture, Kolyvagin's structure theorem for Shafarevich--Tate groups, and the explicit reciprocity law for Heegner points.

math.NT↗

arXiv2018

Variation of anticyclotomic Iwasawa invariants in Hida families

Building on the construction of big Heegner points in the quaternionic setting, and their relation to special values of Rankin-Selberg $L$-functions, we obtain anticyclotomic analogues of the results of Emerton-Pollack-Weston on the variation of Iwasawa invariants in Hida families. In particular, combined with the known cases of the anticyclotomic Iwasawa main conjecture in weight $2$, our results yield a proof of the main conjecture for $p$-ordinary newforms of higher weights and trivial nebentypus.

math.NT↗

arXiv2017

Overconvergent quaternionic forms and anticyclotomic p-adic L-functions

We reinterpret the explicit construction of Gross points given by Chida-Hsieh as a non-Archimedian analogue of the standard geodesic cycle from zero to the infinity on the Poincare upper half plane. This analogy allows us to consider certain distributions, which can be regarded as anticyclotomic p-adic L-functions for modular forms of non-critical slope following the overconvergent strategy a la Stevens. We also give a geometric interpretation of their Gross points for the case of weight two forms. Our construction generalizes those of Bertolini-Darmon, Bertolini-Darmon-Iovita-Spiess, and Chida-Hsieh.

math.NT↗