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Academic Staff

Yu, Chia-Fu

Yu, Chia-Fu

Research Fellow

Research Fields: Arithmetic Algebraic Geometry, Representation Theory,

Email : chiafu@math.sinica.edu.tw

Extension : 628

Dr. Yu's research area are number theory, arithmetic geometry and representation theory. In particular, he is interested in the geometry of Shimura varieties and their applications in representation theory.

  • M.S. University of Pennsylvania 1997
  • B.S. National Taiwan University 1992
  • Ph.D. University of Pennsylvania 1999

  • Ritt Assistant Professor Columbia University 1999 - 2004
  • Visiting Assistant Professor National Center of Theoretic Sciences (NCTS), Taiwan 2002 - 2003
  • Associate Research Fellow Academia Sinica, Taiwan 2004 - 2009
  • Research Fellow Academia Sinica, Taiwan 2009 - Present

  • (with Yasuhiro Terakado, Jiangwei Xue) "On the supersingular locus of Shimura varieties for quaternionic unitary groups.", arXiv:2311.18354, 37 pp. , 2024
  • (with Valentijn Karemaker, Akio Tamagawa) "Uniqueness of indecomposable idempotents in algebras with involution.", arXiv:2402.09323, 12 pp., 2024
  • (with Pei-Xin Liang, Yasuhiro Oki) "Cohomological properties of multinorm-one tori.", arXiv 2310.20133, 26 pp. , 2024
  • (with Jun-Hao Huang, Fan-Yun Hung, Pei-Xin Liang ) "Computing Tate-Shafarevich groups of multinorm one tori of Kummer type", arXiv:2211.11249, 17 pp. To appear in Taiwanese Math. J., 2024
  • "Yasuhiro Terakado and Chia-Fu Yu, Mass formulas and the basic locus of unitary Shimura varieties.", arXiv:2210.04054, 47 pp. , 2024
  • "Chun-Yi Lin and Chia-Fu Yu, On the structure of unitary groups revisited.", Preprint July, 2022. 33 pp. , 2024
  • "Jiangwei Xue and Chia-Fu Yu, Optimal spinor selectivity for quaternion orders.", J. Number Theory , 255, 2024
  • "Tomoyoshi Ibukiyama, Valentijn Karemaker and Chia-Fu Yu, When is a polarised abelian variety determined by its $p$-divisible group?", http://arxiv.org/abs/2205.13180, 39 pp. , 2024
  • "Pei-Xin Liang, Yasuhiro Oki, Hsin-Yi Yang and Chia-Fu Yu, On Tamagawa numbers of CM tori. Appendix by Jianing Li and Chia-Fu", Algebra Number Theory, 18 (3), 2024
  • "Urs Hartl and Chia-Fu Yu, Arithmetic Satake compactifications and algebraic Drinfeld modular forms.", arXiv:2009.13934, 45 pp. , 2024
  • "Jiangwei Xue and C.-F. Yu, Polarized simple superspecial abelian surfaces with real Weil numbers.", arXiv:2009.02729, 59 pp., 2024
  • "Jiangwei Xue and Chia-Fu Yu, Trace formulas for the norm one group of totally definite quaternion algebras ", arXiv:1909.11858v3, 27 pp. , 2024
  • "Jiangwei Xue, Chia-Fu Yu, Yuqiang Zheng, On superspecial abelian surfaces over finite fields III.", Res. Number Theory., 8 (1.9), 1-22, 2022
  • "Chia-Fu Yu, Japanese Dedekind domains are excellent", Taiwanese J. Math., 26 (3), 483-500, 2022
  • "Jiangwei Xue and C.-F. Yu, Polarized simple superspecial abelian surfaces with real Weil numbers: a survey.", Proceedings of RIMS Conference ``Theory and Applications of Supersingular Curves and Supersingular Abelian Varieties'', RIMS K\^oky\^urokuBessatsu. , 0, 39-57, 2022
  • "Yasuhiro Terakado and Chia-Fu Yu, Hecke eigensystems of automorphic forms (mod $p$) of Hodge type and algebraic modular forms.", Math Ann., 382 (1-2), 69-102, 2022
  • "Jia-Wei Guo, Nai-Heng Sheu and C.-F. Yu, Class numbers of CM algebraic tori, CM abelian varieties and components of unitary Shimura varieties.", Nagoya Math Journal., 245, 74-99, 2022
  • "Chun-Yi Lin and Chia-Fu Yu, Dieudonn\'e determinants and subgroups of general linear groups over division rings revisited.", Bull. Inst. Math. Acad. Sin. (N.S.), 16 (1), 21-47, 2021
  • "Valentijn Karemaker, Fuetaro Yobuko and Chia-Fu Yu, Mass formula and Oort's conjecture for supersingular abelian threefolds.", Adv. in Math. 386 (2021), 107812, 1-52, 2021
  • "Xu Shen, Chia-Fu Yu, Chao Zhang, EKOR strata for Shimura varieties with parahoric level structure.", Duke Math. J. , 170 (14), 3111-3236, 2021
  • "Jiangwei Xue and C.-F. Yu, On superspecial abelian surfaces and type numbers of totally definite quaternion algebras, ", Indiana Univ. Math. J., 70 (2), 783-810, 2021
  • "Qun Li, Jiangwei Xue and C.-F. Yu, Unit groups of maximal Orders in totally definite quaternion algebras over real quadratic fields. ", Trans. Amer. Math. Soc. , 374 (8), 5349-5403, 2021
  • " J. Xue and C.-F. Yu, On counting certain abelian varieties over finite fields.", Acta Math. Sinica (Engl. Ser.) 37 (2021), no. 1, 205--228., 37 (1), 205-228, 2021
  • "C.-F. Yu, Reduction of the moduli schemes of abelian varieties with definite quaternion multiplication.", Annales de l'Institut Fourier (Grenoble), 76 pp., 71 (2), 539-613, 2021
  • "Jianing Li and Chia-Fu Yu, The Chevalley-Gras formula over global fields,", J. Theor. Nombres Bordeaux, 32, 525-543, 2020
  • "C.-F. Yu, C.-L. Chai and F. Oort, Stratifying Lie strata of Hilbert modular varieties. ", Taiwanese J. Math. , 24 (6), 1307-1352, 2020
  • "Jiangwei Xue and Chia-Fu Yu, On counting certain principally polarized superspecial abelian surfaces over $\mathbb{F}_p$", Proceedings of ``Automorphic forms, automorphic representations and related topics'', RIMS K\^oky\^uroku, 14 pp. , 2020
  • " J. Xue, T.-C. Yang and C.-F. Yu, On superspecial abelian surfaces over finite fields II. ", J. Math. Soc. Japan, 72 (1), 303-331, 2020
  • "C.-F. Yu, A note on supersingular abelian varieties.", Bull. Inst. Math. Acad. Sin. (N.S.), 15 (1), 9-32, 2020
  • "C.-F. Yu, Chow's theorem for semi-abelian varieties and bounds for splitting fields of algebraic tori ", Acta Math. Sin. (Engl. Ser.), 35 (9), 1453-1463, 2019
  • "Qun Li, Jiangwei Xue and C.-F. Yu, Reduced unit groups in totally definite quaternion algebras over real quadratic fields. Proceedings of "Analytic and algebraic theory of automorphic forms".", RIMS K\^oky\^uroku, 2100, 80-93, 2019
  • "J. Xue, T.-C. Yang and C.-F. Yu, Supersingular abelian surfaces and Eichler's class number formula", Asian J. Math., 23 (4), 651-680, 2019
  • "C.-F. Yu, A remark on Chevalley's ambiguous class number formulas", arXiv:1412.1458. 3 pp. , 2018
  • " C.-F. Yu, On arithmetic of the superspecial locus ", Indiana Univ. Math. J., 67 (4), 1341-1382, 2018
  • "C.-F. Yu, On fields of definition of components of Siegel supersingular locus", Proc. Amer. Math. Soc. , 145 (12), 5053-5058, 2017
  • "C.-F. Yu, Notes on locally free class groups.", Bull. Inst. Math. Acad. Sin. (N.S.) , 12 (2), 125-139, 2017
  • "C.-F. Yu, Abelian varieties over finite fields as basic abelian varieties. ", Forum Math. , 29 (2), 489-500, 2017
  • "C.-F. Yu, On existence and density of the ordinary locus of certain Shimura varieties.", Proceedings of the 6th International Congress of Chinese Mathematicians, ALM, 36, 361-379, 2017
  • "J. Xue, T.-C. Yang and C.-F. Yu, Numerical invariants of totally imaginary quadratic ${\mathbb Z}[\sqrt{p}]$-orders.", Taiwanese J. Math., 20 (4), 723-741, 2016
  • "C.-F. Yu, On non-emptiness of basic loci of Shimura varieties. ", MFO Workshop on Reductions of Shimura Varieties.~Math. F.~Oberwolfach Report No. 39/2015, 2016
  • "J. Xue, T.-C. Yang and C.-F. Yu, On superspecial abelian surfaces over finite fields. ", Doc. Math., 21, 1607-1643, 2016
  • " J. Xue and C.-F. Yu, Abelian varieties without a prescribed Newton polygon reduction.", Proc. Amer. Math. Soc. , 143 (6), 2339-2345, 2015
  • " T.-C. Yang and C.-F. Yu, Monomial, Gorenstein and Bass orders.", J. Pure Appl. Algebra., 219, 767-778, 2015
  • "J. Xue and C.-F. Yu, Endomorphism algebras of factors of certain hypergeometric Jacobians.", Trans. Amer. Math. Soc., 367, 8071-8106, 2015
  • "C.-F. Yu, Variants of mass formulas for definite division algebras.", J. Algebra, 422, 166-186, 2015
  • "C.-F. Yu, A Note on the Mumford-Tate conjecture for CM abelian varieties", Taiwanese J. Math., 19, 1073-1084, 2015
  • "Fu-Tsun Wei and C.-F. Yu, Class numbers of definite central simple algebras over global function fields.", Int. Math. Res. Not. , 2015 (11), 3525-3575, 2015
  • "C.-F. Yu, Notes on density of the ordinary locus", Bull. Inst. Math. Acad. Sin. (N.S.), 9, 711-733, 2014
  • " H. Wang, J. Xue and C.-F. Yu, Fixed points and homology of superelliptic Jacobians. ", Math. Z., 278, 169-189, 2014
  • "S.-C. Shih, T.-C. Yang and C.-F. Yu, Embeddings of fields into simple algebras over global fields.", Asian J. Math., 18, 365-386, 2014
  • "C.-F. Yu, Shuffle structures on KR strata. ", MFO Workshop on Reductions of Shimura Varieties. Math. F. Obwerwolfach Report No. 32/2012, 1995-1999, 2013
  • "C.-F. Yu, Endomorphism algebras of QM abelian surfaces.", J. Pure App. Algebra., 217, 907-914, 2013
  • "C.-F. Yu, Characteristic polynomials of central simple algebras.", Taiwanese J. Math., 17 (1), 351-359, 2013
  • "C.-F. Yu, Embeddings of fields into simple algebras: generalizations and applications.", J. Algebra, 368, 1-20, 2012
  • "F.-T. Wei and C.-F. Yu, Mass formula of division algebras over function fields. ", J. Number Theory, 132, 1170-1185, 2012
  • "C.-F. Yu, On Hermitian forms over dyadic non-maximal local orders.", Pure Appl. Math. Q. , 8 (4), 1117-1146, 2012
  • "C.-F. Yu, Superspecial abelian varieties over prime finite fields. ", J. Pure and Appl. Algebra, 216, 1418-1427, 2012
  • "U. Goertz and C.-F. Yu, The supersingular locus in Siegel modular varieties with Iwahori level structure. ", Math. Ann., 353, 465-498, 2012
  • "C.-F. Yu, On the existence of maximal orders. ", Int. J. Number Theory, 7 (8), 2091-2114, 2011
  • "C.-F. Yu, Geometry of the Siegel modular threefold with paramodular level structure. ", Proc. Amer. Math. Soc., 139 (9), 3181-3190, 2011
  • "C.-F. Yu, On finiteness of endomorphism rings of abelian varieties", Math. Res. Letters, 17, 357-370, 2010
  • "C.-F. Yu, Kottwitz-Rapoport strata of the Siegel moduli spaces. ", Taiwanese J. Math., 14, 2343-2364, 2010
  • "U. Görtz and C.-F. Yu, Supersingular Kottwitz-Rapoport strata and Deligne-Lusztig varieties", J. Inst. Math Jussieu, 9 (2), 357-390, 2010
  • "C.-F. Yu, Simple mass formulas on Shimura varieties of PEL-type. ", Forum. Math., 22 (3), 565-582, 2010
  • "C.-F. Yu and J.-D. Yu, Mass formula for supersingular abelian surfaces. ", J. Algebra, 322, 3733-3743, 2009
  • "C.-F. Yu, Irreducibility of the Hilbert-Blumenthal moduli spaces with parahoric level structure. ", J. Reine Angew. Math., 635, 187-211, 2009
  • "C.-F. Yu, An exact geometric mass formula. ", Int. Math. Res. Not., 2008 (113), 1-11, 2008
  • "C.-F. Yu, Irreducibility and $p$-adic monodromies on the Siegel moduli spaces. ", Adv. Math., 218, 1253-1285, 2008
  • "C.-F. Yu, Leaves on Shimura varieties.", Proceedings of the ICCM, 0, 630-661, 2007
  • "C.-F. Yu, Construction of Galois covers of curves with groups of ${\rm SL_2}$-type.", C. R. Acad. Sci. Paris Sér. I. Math, 345, 77-80, 2007
  • "C.-F. Yu, The supersingular loci and mass formulas on Siegel modular varieties. Doc. Math. 11 (2006), 449 -- 468", 2006
  • "C.-F. Yu, Discrete Hecke orbit problems for Hilbert-Blumenthal varieties.", NCTS/TPE-Math Technical Report 2006-1, 20 pp, 1-20, 2006
  • "C.-F. Yu, Basic points in the moduli spaces of PEL-type.", MPIM-preprint 2005-113, 11 pp, 2005
  • "C.-F. Yu, On the slope stratification of certain Shimura varieties. Math. Z. 251 (2005), 859 --873.", 2005
  • "C.-F. Yu, On the mass formula of supersingular abelian varieties with real multiplications", J. Australian Math. Soc., 78, 373-392, 2005
  • (with C.-L. Chai) "Notes on Cartier theory, Barsotti-Tate groups, Hecke orbits and canonical coordinates, lectures presented in the 2004 AS-NCTS joint seminar on Arithmetic and Algebraic Geometry, Number Theory, and Representation Theory, 12/30-31/2004, 1/6-7/2005. ", 2004
  • "C.-F. Yu, Irreducibility of Siegel moduli spaces with parahoric level structure ", Int. Math. Res. Not., 48, 2593-2597, 2004
  • "C.-F. Yu and J. Yu, Mass formula for supersingular Drinfeld modules", C. R. Acad. Sci. Paris S\'er. I Math, 338, 905-908, 2004
  • "C.-F. Yu, The isomorphism classes of abelian varieties of CM type", J. Pure Appl. Algebra, 187, 305-319, 2004
  • "Zeta functions of modular curves. NCTS Lecture Notes, 2003. ", NCTS Lecture Notes, 2003
  • "C.-F. Yu, On reduction of Hilbert-Blumenthal varieties", Annales de l'Institut Fourier (Grenoble), 53, 2105-2154, 2003
  • "C.-F. Yu, On the supersingular locus in Hilbert-Blumenthal 4-folds", J. Algebraic Geom., 12, 653-698, 2003
  • "Notes on Intersection cohomology, $L^2$-cohomology and $L$-functions of Hilbert-Blumenthal varieties (following the work of Brylinski and Labesse), NCTS Lecture Notes, 2002, 111 pp. ", NCTS Lecture Notes, 111-, 2002
  • "C.-F. Yu, Lifting abelian varieties with additional structure. Math. Z. 242 (2002) 427--441. ", 2002
  • "C.-F. Yu, On the supersingular locus of Hilbert-Blumenthal 4-folds, Thesis, University of Pennsylvania (1999), 76 pp ", 1999
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