Research

Preprints

・A refined non-vanishing of the p-adic logarithm of a rational point on an abelian variety (with C. Skinner and X. Wan), arXiv.

・ A local sign decomposition for symplectic self-dual Galois representations of rank two (with S. Kobayashi, K. Nakamura, K. Ota), arXiv.

・ Mod l non-vanishing of self-dual Hecke L-values over CM fields and applications (with W. He, Y. Tian, X. Ye), arXiv.

・ Generation of Hecke fields by squares of cyclotomic twists of modular L-values (with V. Blomer, P. Michel, J.-H. Min), arXiv.

・ Zeta elements for elliptic curves and applications (with C. Skinner, Y. Tian, X. Wan), arXiv.

・Hecke L-values, definite Shimura sets and mod l non-vanishing (with W. He, S. Kobayashi, K. Ota), arXiv.

・A p-converse theorem for CM elliptic curves (with C. Skinner), arXiv, an appendix to `Integers expressible as the sum of two rational cubes' by L. Alpoge, M. Bhargava and A. Shnidman, arXiv, cf.

・ Horizontal variation of Tate-Shafarevich groups (with H. Hida, Y. Tian), arXiv.

・p-rigidity and p-independence of quaternionic modular forms modulo p.

Publications

・Anticyclotomic Iwasawa theory of abelian varieties of GL(2)-type at non-ordinary primes II (with K. Buyukboduk, A. Lei), Algebra Number Theory, arXiv.

・ Non-vanishing of Kolyvagin systems and Iwasawa theory (with F. Castella, G. Grossi, C. Skinner), Cambridge J. Math., arXiv.

・ A rank zero p-converse to a theorem of Gross-Zagier, Kolyvagin and Rubin (with Y. Tian), Ann. of Math., arXiv, cf.

・ The p-adic valuation of local resolvents, generalized Gauss sums and anticyclotomic Hecke L-values of imaginary quadratic fields at inert primes (with S. Kobayashi, K. Ota), American J. Math, arXiv.

・ Base change and Iwasawa Main Conjectures for GL_2 (with F. Castella, C. Skinner), IMRN, arXiv, journal.

・On the Frobenius fields of abelian varieties over number fields (with H. Hida, S. Lai), Algebra Number Theory, arXiv.

・Dimension of the deformation space of ordinary representations in the cyclotomic limit (with L. Clozel, B. Mazur), Pure Appl. Math. Q., arXiv, journal.

・On the Tate-Shafarevich group of CM elliptic curve over anticyclotomic Z_p-extensions at inert primes (with S. Kobayashi, K. Ota), Proceedings of the Bertolinifest, pdf.

・Kato's epsilon conjecture for anticyclotomic CM deformations at inert primes (with S. Kobayashi, K. Ota, S. Yasuda), J. Number Theory (Biennial volume), pdf, journal.

・The conjecture of Birch and Swinnerton-Dyer for certain elliptic curves with complex multiplication (with M. Flach), Cambridge J. Math., 12 (2024), no. 2, 357-415, pdf, journal.

・Anticyclotomic Iwasawa theory of abelian varieties of GL(2)-type at non-ordinary primes (with K. Buyukboduk, A. Lei), Adv. Math., 439 (2024), 109465, pdf, journal.

・p-adic L-functions and rational points on CM elliptic curves at inert primes (with S. Kobayashi, K. Ota), J. Inst. Math. Jussieu, 23 (2024), no. 3, 1417-1460, journal.

・Ordinary deformations are unobstructed in the cyclotomic limit (with L. Clozel), Asian J. Math., 27 (2023), no. 3, 405-422, pdf, journal.

・A note on rank one quadratic twists of elliptic curves and non-degeneracy of p-adic regulators at Eisenstein primes (with C. Skinner), Proc. Amer. Math. Soc., Ser B. 10,13-32 (2023), pdf, journal.

・p-Selmer groups and rational points on CM elliptic curves (with F. Castella, C. Skinner, Y. Tian), Ann. Math. Que. 46 (2022), no. 2, 325-346, journal.

・ Rubin's conjecture on local units in the anticyclotomic tower at inert primes (with S. Kobayashi, K. Ota), Ann. of Math. (2) 194 (2021), no. 3, 943-966, journal.

・ A proof of Perrin-Riou's Heegner point main conjecture (with F. Castella, C.-H. Kim), Algebra Number Theory 7 (2021), no. 15, 1627-1653, pdf, journal.

・ On the non-vanishing of p-adic heights for CM abelian varieties and arithmetic of Katz p-adic L-functions (with D. Disegni), Ann. Inst. Fourier (Grenoble) 70 (2020), no. 5, 2077-2101, pdf, journal.

・ Quantitative non-vanishing of Dirichlet L-values modulo p (with H.-S. Sun), Math. Ann. 378 (2020), no. 1-2, 317-358, pdf, journal.

・ p-converse to a theorem of Gross-Zagier, Kolyvagin and Rubin (with Y. Tian), Invent. Math. 220 (2020), no. 1, 211-253, pdf, journal.

・ On the non-triviality of p-adic Abel-Jacobi image of Heegner cycles modulo p, I: modular curves, J. Algebraic Geom. 29 (2020), no. 2, 329-371, pdf, journal.

・ Horizontal non-vanishing of Heegner points and toric periods (with Y. Tian), Adv. Math. 362 (2020), 106938, 35 pp, pdf, journal.

・ p-rigidity and Iwasawa µ-invariants (with H. Hida), Algebra Number Theory 11 (2017), no. 8, 1921-1951, pdf, journal.

・ On the non-triviality of p-adic Abel-Jacobi image of Heegner cycles modulo p, II: Shimura curves, J. Institut Math. Jussieu 16 (2017), no. 1, 189-222, pdf, journal.

・ Andre-Oort conjecture and non-vanishing of central L-values over Hilbert class fields (with H. Hida), Forum Math. Sigma 4 (2016), e20, 26 pp, journal.

・ An l≠p-interpolation of genuine p-adic L-functions, Res. Math. Sci. 3 (2016), Paper No. 16, 26 pp, journal.

・ On the µ-invariant of the cyclotomic derivative of Katz p-adic L-function, J. Inst. Math. Jussieu 14 (2015), no. 1, 131-148, pdf, journal.

・ The vanishing of the µ-invariant of p-adic Hecke L-function for CM fields (with M.-L. Hsieh), IMRN no. 5 (2013), 1014-1027, journal.

Thesis

On the non-triviality of arithmetic invariants modulo p, June 2015, eScholarship.

Expository

・A p-adic Waldspurger formula and the conjecture of Birch and Swinnerton-Dyer, J. Indian Inst. Sci., 2022, pdf, journal.

・The even parity Goldfeld conjecture: congruent number elliptic curves (with Y. Tian), J. Number Theory (Biennial volume), 2022, pdf, journal.

・ The Birch and Swinnerton-Dyer conjecture: a brief survey (with C. Skinner, Y. Tian), Proc. Sympos. Pure Math., 2021, pdf, book.

・ p-converse to a theorem of Gross-Zagier, Kolyvagin and Rubin, Algebraic Number Theory, Oberwolfach reports, 2018, pdf.

・ Horizontal non-vanishing of Rankin-Selberg L-values, Prime Numbers and Representation Theory, Lecture Series of Modern Number Theory: volume 2, 2017, pdf.

・ Non-triviality of generalised Heegner cycles over anticyclotomic towers: a survey, Chapter 8 of p-Adic Aspects of Modular Forms, World Scientific, 2016, pdf, book.

・ On the non-triviality of generalised Heegner cycles modulo p, Algebraic Number Theory, Oberwolfach reports, Report No. 32/2014, pdf.