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# Yu, Chia-Fu

 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. Email : chiafu AT math.sinica.edu.tw Phone:+886 2 2368-5999 ext. 628 Fax: +886 2 2368-9771

 Publications 1. C.-F. Yu, On the supersingular locus of Hilbert-Blumenthal 4-folds, Thesis, University of Pennsylvania (1999), 76 pp 2. C.-F. Yu, Lifting abelian varieties with additional structure. Math. Z. 242 (2002) 427--441., , 0-0 3. On the supersingular locus in Hilbert-Blumenthal 4-folds, J. Algebraic Geom. , 12(2003), 653-698 4. On reduction of Hilbert-Blumenthal varieties, Annales de l'Institut Fourier (Grenoble) , 53(2003), 2105-2154 5. The isomorphism classes of abelian varieties of CM type, J. Pure Appl. Algebra , 187(2004), 305-319 6. (with J. Yu) Mass formula for supersingular Drinfeld modules, C. R. Acad. Sci. Paris S\'er. I Math , 338(2004), 905-908 7. Irreducibility of Siegel moduli spaces with parahoric level structure, Int. Math. Res. Not. , 48(2004), 2593-2597 8. On the mass formula of supersingular abelian varieties with real multiplications, J. Australian Math. Soc. , 78(2005), 373-392 9. C.-F. Yu, On the slope stratification of certain Shimura varieties. Math. Z. 251 (2005), 859 --873., , 0-0 10. C.-F. Yu, The supersingular loci and mass formulas on Siegel modular varieties. Doc. Math. 11 (2006), 449 -- 468, , 0-0 11. C.-F. Yu, Construction of Galois covers of curves with groups of ${\rm SL_2}$-type., C. R. Acad. Sci. Paris S{\'e}r. I. Math , 345(2007), 77-80 12. C.-F. Yu, Leaves on Shimura varieties., Proceedings of the ICCM , II(2007), 630-661 13. C.-F. Yu, Irreducibility and $p$-adic monodromies on the Siegel moduli spaces., Adv. Math. , 218(2008), 1253-1285 14. C.-F. Yu, An exact geometric mass formula., Int. Math. Res. Not. , 2008(2008), no. 113, 1-11 15. C.-F. Yu, Irreducibility of the Hilbert-Blumenthal moduli spaces with parahoric level structure., J. Reine Angew. Math. , 635(2009), 187-211 16. C.-F. Yu and J.-D. Yu, Mass formula for supersingular abelian surfaces., J. Algebra , 322(2009), 3733-3743 17. U. G\"ortz and C.-F. Yu, Supersingular Kottwitz-Rapoport strata and Deligne-Lusztig varieties, J. Inst. Math Jussieu , 9(2010), 357-390 18. C.-F. Yu, Simple mass formulas on Shimura varieties of PEL-type., Forum. Math. , 22(2010), 565-582 19. C.-F. Yu, On finiteness of endomorphism rings of abelian varieties, Math. Res. Letters , 17(2010), 357-370 20. C.-F. Yu, Kottwitz-Rapoport strata of the Siegel moduli spaces., Taiwanese J. Math. , 14(2010), 2343-2364 21. C.-F. Yu, Geometry of the Siegel modular threefold with paramodular level structure., Proc. Amer. Math. Soc. , 139(2011), 3181-3190 22. C.-F. Yu, On the existence of maximal orders., Int. J. Number Theory , 7(2011), 2091-2114 23. C.-F. Yu, Superspecial abelian varieties over prime finite fields., J. Pure and Appl. Algebra , 216(2012), 1418-1427 24. F.-T. Wei and C.-F. Yu, Mass formula of division algebras over function fields., J. Number Theory , 132(2012), 1170-1185 25. C.-F. Yu, On Hermitian forms over dyadic non-maximal local orders., Pure Appl. Math. Q. , 8(2012), 1117-1146 26. C.-F. Yu, Embeddings of fields into simple algebras: generalizations and applications., J. Algebra , 368(2012), 1-20 27. U. Goertz and C.-F. Yu, The supersingular locus in Siegel modular varieties with Iwahori level structure., Math. Ann. , 353(2012), 465-498 28. C.-F. Yu, Endomorphism algebras of QM abelian surfaces., J. Pure App. Algebra. , 217(2013), 907-914 29. C.-F. Yu, Characteristic polynomials of central simple algebras., Taiwanese J. Math. , 17(2013), 351-359 30. C.-F. Yu, Shuffle structures on KR strata., MFO Workshop on Reductions of Shimura Varieties. Math. F. Obwerwolfach Report No. 32/2012 (2013), 1995-1999 31. S.-C. Shih, T.-C. Yang and C.-F. Yu, Embeddings of fields into simple algebras over global fields., Asian J. Math. , 18(2014), 365-386 32. C.-F. Yu, Notes on density of the ordinary locus, Bull. Inst. Math. Acad. Sin. (N.S.) , 9(2014), 711-733 33. H. Wang, J. Xue and C.-F. Yu, Fixed points and homology of superelliptic Jacobians., Math. Z. , 278(2014), 169-189 34. J. Xue and C.-F. Yu, Abelian varieties without a prescribed Newton polygon reduction., Proc. Amer. Math. Soc. , 143(2015), 2339-2345 35. T.-C. Yang and C.-F. Yu, Monomial, Gorenstein and Bass orders., J. Pure Appl. Algebra. , 219(2015), 767-778 36. C.-F. Yu, Variants of mass formulas for definite division algebras., J. Algebra , 422(2015), 166-186 37. C.-F. Yu, A Note on the Mumford-Tate conjecture for CM abelian varieties, Taiwanese J. Math. , 19(2015), 1073-1084 38. J. Xue and C.-F. Yu, Endomorphism algebras of factors of certain hypergeometric Jacobians., Trans. Amer. Math. Soc. , 367(2015), 8071-8106 39. Fu-Tsun Wei and C.-F. Yu, Class numbers of definite central simple algebras over global function fields., Int. Math. Res. Not. , 2015(2015), no. 11, 3525-3575 40. 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) 41. J. Xue, T.-C. Yang and C.-F. Yu, Numerical Invariants of Totally Imaginary Quadratic ${\mathbb Z}[\sqrt{p}]$-orders., Taiwanese J. Math. , 20(2016), 723-741 42. J. Xue, T.-C. Yang and C.-F. Yu, On superspecial abelian surfaces over finite fields., Doc. Math. , 21(2016), 1607-1643 43. 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(2017), 361-379 44. C.-F. Yu, Abelian varieties over finite fields as basic abelian varieties., Forum Math. , 29(2017), 489-500 45. C.-F. Yu, Notes on locally free class groups., Bull. Inst. Math. Acad. Sin. (N.S.) 12 (2017), No. 2 125--139. (2017) 46. C.-F. Yu, On fields of definition of components of Siegel supersingular locus, Proc. Amer. Math. Soc. 145 no 12 (2017), 5053--5058. (2017) 47. C.-F. Yu, On arithmetic of the superspecial locus, arXiv:1210.1120v2, 35 pp. To appear in Indiana Univ. Math. J. (2018), 0-0 48. Qun Li, Jiangwei Xue and C.-F. Yu, Reduced unit groups in totally definite quaternion algebras over real quadratic fields, Proceedings of the 2018 RIMS conference "Analytic and Arithmetic Theory of Automorphic Forms", 18 pp (2018) 49. J. Xue, T.-C. Yang and C.-F. Yu, Supersingular abelian surfaces and Eichler's class number formula, arXiv:1404.2978v2. 29 pp. To appear in Asian J. Math. (2019), 0-0
 Lecture Notes 1. 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. 2. Zeta functions of modular curves. NCTS Lecture Notes, 2003., NCTS Lecture Notes (2003) 3. (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)
 Preprints 1. C.-F. Yu, Discrete Hecke orbit problems for Hilbert-Blumenthal varieties. 2. C.-F. Yu, Basic points in the moduli spaces of PEL-type., MPIM-preprint 2005-113, 11 pp , 0-0 3. C.-F. Yu, Reduction of the moduli schemes of abelian varieties with definite quaternion multiplication: the minimal case., arXiv:1306.1400. 52 pp. Submitted. (2018), 0-0 4. C.-F. Yu, A remark on Chevalley's ambiguous class number formulas, arXiv:1412.1458. 3 pp. Submitted (2018) 5. C.-F. Yu, A note on supersingular abelian varieties., arXiv:1412.7107v2. 14 pp. Submitted (2018) 6. J. Xue, T.-C. Yang and C.-F. Yu, On superspecial abelian surfaces over finite fields II., arXiv:1801.09374. 21 pp. Submitted (2018) 7. J. Xue and C.-F. Yu, Counting abelian varieties over finite fields., arXiv:1801.00229, 17 pp. Submitted (2018)