Publications Minhyong Kim Journal

Publications

Minhyong Kim

Journal articles:

–Numerically positive line bundles on arithmetic varieties. Duke Math. J. 61 (1990), no. 3, pp. 805–821. –Small points on constant arithmetic surfaces. Duke Math. J. 61 (1990), no. 3, pp. 823–833. –Weights in cohomology groups arising from hyperplane arrangements. Proc. Amer. Math. Soc. 120 (1994), no.3, pp. 697–703. –A Lefschetz trace formula for equivariant cohomology. Ann. Sci. Ecole Norm. Sup. 28 (1995), Series 4, no. 6, pp. 669–688. –Pfaﬃan equations and the Cartier operator. Compositio Math. 105 (1997), no. 1, pp. 55–64. –Geometric height inequalities and the Kodaira-Spencer map. Composito Math. 105 (1997), no. 1, pp. 43–54 (1997). –On the Kodaira-Spencer map and stability. Internat. Math. Res. Not. (1997), no. 9, pp. 417–419. –Purely inseparable points on curves of higher genus. Math. Res. Lett. 4 (1997), no. 5, pp. 663–666. –ABC inequalities for some moduli spaces of log-general type. Math. Res. Lett. 5 (1998), no. 5, pp. 517–522. –On reductive group actions and ﬁxed-points. Proc. Amer. Math. Soc. 126 (1998), no. 11, pp. 3397–3400. –Diophantine approximation and deformations (with D. Thakur and F. Voloch). Bull. Soc. Math. Fr. 128 (2000), no. 4, pp. 585–598. –Crystalline sub-representations and Neron models (with S. Marshall). Math. Res. Lett. 7, no. 5-6, pp. 605–614 (2000). –A remark on potentially semi-stable representations (with K. Joshi). Math. Zeit., no. 241, pp. 479–483 (2002). –Topology of algebraic surfaces and reduction modulo p (with D. Joe). Internat. Math. Res. Not. (2002), no. 28, pp. 1505–1508. –The Picard-Lefschetz formula and a conjecture of Kato (with C. Consani), Math. Res. Lett. 9 (2002), no. 5-6, pp. 621–631.

1 –Relating decision and search algorithms for rational points on aﬃne plane curves of higher genus. Arch. Math. Logic 42 (2003), no. 6, pp. 563–568. –A De Rham-Witt approach to crystalline rational homotopy theory (with R. Hain). Compositio Math. 140 (2004), no. 5, pp. 1245–1276. –The Hyodo-Kato theorem for rational homotopy types (with R. Hain). Math. Res. Lett. 12 (2005), no. 2-3, pp. 155–169. –The motivic fundamental group of P1 \{0, 1, ∞} and the theorem of Siegel. Invent. Math. 161 (2005), no. 3, pp. 629–656. –The l-component of the unipotent Albanese map (with A. Tamagawa). Mathematische Annalen, 340 (2008), no. 1, pp. 223-235. –The unipotent Albanese map and Selmer varieties for curves. Publ. Res. Inst. Math. Sci. 45 (2009), no. 1, pp. 89–133. (Proceedings of special semester on arithmetic geometry, Fall, 2006.) –Massey products for elliptic curves of rank one. J. Amer. Math. Soc. 23 (2010), 725-747. –p-adic L-functions and Selmer varieties associated to elliptic curves with complex multiplication. Annals of Math. 172 (2010), no. 1, 751–759. –Selmer varieties for curves with CM Jacobians (with J. Coates). Kyoto Journal of Mathematics (special issue in memory of Nagata), 50 (2010), no. 4, 827–852. –Appendix and erratum: Massey products for elliptic curves of rank one (with J. Balakrishnan and K. Kedlaya). J. Amer. Math. Soc. 24 (2011), no. 1, 281-291. –Heat-Mapping: A Robust Approach Toward Perceptually Consistent Mesh Segmentation (with Yi Fang, Mengtian Sun, and Karthik Ramani). IEEE Computer Vision and Pattern Recognition (CVPR), pp 2145–2152 (2011). –Tangential localization for Selmer varieties. Duke Math. J. 161 (2012), no. 2, 173199. –On the 2-part of the Birch-Swinnerton-Dyer conjecture for elliptic curves with complex multiplication (with John Coates, Zhibin Liang and Chunlai Zhao). Muenster Journal of Mathematics 7 (2014) (volume in honor of Peter Schneider), 83–103. –A p-adic criterion for good reduction of curves (with Fabrizio Andreatta and Adrian Iovita). Duke Math. J. 164 (2015), no. 13, 2597–2642. –Abelian Arithmetic Chern-Simons Theory and Arithmetic Linking Numbers (with H. Chung, D. Kim, G.Pappas, J. Park, H. Yoo). International Mathematics Research Notices, Vol. 2017, pp. 1–29 –A non-abelian conjecture of Tate-Shafarevich type for hyperbolic curves (with Jennifer Balakrishnan, Ishai Dan-Cohen, and Stefan Wewers.). Mathematische Annalen October 2018, Volume 372, Issue 1–2, pp 369–428.

2 –Arithmetic Gauge Theory: A Brief Introduction. Modern Physics Letters A, Vol. 33, No. 29 (2018) Chapters in books: The mathematical structure of characters and modularity (with J. Kim). Characters, G. Wagner ed., Academic Press (2000). –The non-abelian (non-linear) method of Chabauty. Noncommutative Geometry and Number Theory: Where Arithmetic meets Geometry and Physics. 179–185, Aspects Math., E37, Vieweg, Wiesbaden, 2006., C. Consani and C. Marcolli (eds.). –A remark on fundamental groups and effective Diophantine methods for hyperbolic curves. Number theory, Analysis and Geometry. 355–368, D. Goldfeld, J. Jorgenson, P. Jones, D. Ramakrishnan, K. Ribet and J. Tate (eds.), Springer, New York (2012). –Classical motives and motivic L-functions. Autour des motifs–Ecole´ d’été Franco-Asiatique de GéométrieAlgébriqueet de Théorie des Nombres. Volume I, 1–25, Panor. Synthèses,29, Soc. Math. France, Paris (2009). –Galois theory and Diophantine geometry. Non-abelian fundamental groups and Iwasawa theory, 162–187, London Math. Soc. Lecture Note Ser., 393, Cambridge Univ. Press, Cambridge (2012). –Diophantine geometry and non-abelian reciprocity laws I. Elliptic curves, modular forms and Iwasawa theory, 311–334, Springer Proc. Math. Stat., 188, Springer, Cham, 2016. –Principal bundles and reciprocity laws in number theory. Proceedings of the Symposia in Pure Mathematics: Algebraic Geometry: Salt Lake City 2015. vol. 97, T. de Fernex, B. Hassett, M. Mustata, M. Olsson, M. Popa and R. Thomas (eds.) (2018). –Arithmetic Gauge Theory: a brief introduction. Topology and Physics, C.N.Yang, M.L.Ge and Y.H.He (Eds.) World Scientific (2019) –Arithmetic Chern-Simons Theory II. (with H. Chung, D. Kim, J. Park, H. Yoo).To be published in the Proceedings of the Simons Symposium on p-adic Hodge theory. Preprint available as arXiv:1609.03012v3

Preprints: –Arithmetic Chern-Simons Theory I. Preprint available as arXiv:1510.05818v3. –Mirror symmetry, mixed motives, and ζ(3) (with W. Yang), Preprint available as arXiv:1710.02344v2

Expository Articles: –Diophantine geometry as Galois theory in the mathematics of Serge Lang, in ‘The Mathematical Contributions of Serge Lang,’ Notices of the Amer. Math. Soc. (2007) 54, no.4, pp. 490-494.

3 –Fundamental groups and Diophantine geometry. Central European Journal of Mathematics 2010, 8(4), 633–645. –On the work of Bao Chau Ngo (with Sugwoo Shin). Newsletter of the Korean Mathematical Society 133, September, 2010, pp. 11–17. –On relative computability for curves. Asia-Paciﬁc Mathematics Newsletter 3 (2013), no.2, pp. 16–20. –Mathematics and Occam’s Razor (with P. B. Shalen and D. Yang). Mathematical Intellgencer, special volume for ICM 2014. Books: –Prime Fantasy. Banni Publishing, Seoul (2013) –Father’s Mathematical Journey. Eunhaeng-namu Publishing, Seoul (2014). –On the Learning of Mathematics. (with Taekyung Kim) Eunhaeng-namu Publishing, Seoul (2016). –The Moment You Need Mathematics. Inﬂuential Inc., Seoul (2018). Books edited: –Non-abelian fundamental groups and Iwasawa theory (with John Coates, Florian Pop, Peter Schneider, and Mohamed Saidi), London Math. Soc. Lecture Note Ser., 393, Cambridge Univ. Press, Cambridge (2012). –Automorphic Forms and Galois Representations I, II (co-edited with Fred Diamond and Payman Kassaei). Cambridge University Press (2014).

Book in preparation: Archimedes (with Jonathan Prag). To be published by Book 24, Inc.

Work publicly available at the mathematics e-print archive, arxiv.org (not for separate publication): –Diophantine equations in two variables. math.NT/0210329. –Why everyone should know number theory. math.NT/0210327. –Height inequalities and canonical class inequalities. math.AG/0210330. –Torsion points on modular curves and Galois theory (with K. Ribet). math.NT/0305281. –On Szpiro’s inequality for higher genus curves. math.NT/0210356. –A vanishing theorem for Fano varieties in positive characteristic. math.AG/0201183.