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Books

  1. Motivic integration, the McKay correspondence and wild ramification, in preparation, version:2021-11-11.

  2. A Glimpse into University Math Through Games, Kyoritsu Shuppan (Dec. 2018).

Papers

My papers on Google Scholar

  1. Quotient singularities by permutation actions are canonical,
    arXiv:2408.13504.

  2. Motivic versions of mass formulas by Krasner, Serre and Bhargava,
    arXiv:2408.13481.

  3. The Manin conjecture for toric stacks,
    joint work with Ratko Darda,
    arXiv:2311.02012.

  4. Higher Jacobian ideals, contact equivalence and motivic zeta functions,
    joint work with Quy Thuong Lê,
    arXiv:2310.07976, to appear in Revista Matemática Iberoamericana.

  5. Non-commutative resolutions of linearly reductive quotient singularities,
    joint work with Christian Liedtke,
    The Quarterly Journal of Mathematics, Volume 75, Issue 3, 969–985, (Jun. 2024). DOI:https://doi.org/10.1093/qmath/haae033

  6. F-blowups and essential divisors for toric varieties,
    joint work with Enrique Chávez-Martínez and Daniel Duarte,
    arXiv:2304.13247.

  7. Log centres of noncommutative crepant resolutions are Kawamata log terminal: remarks on a paper of Stafford and Van den Bergh,
    joint work with Colin Ingalls, Contemporary Mathematics 801, Recent Advances in Noncommutative Algebra and Geometry, 143-154, (Jul. 2024). Webpage of the entire volume

  8. Quantitative inverse Galois problem for semicommutative finite group schemes,
    joint work with Ratko Darda,
    arXiv:2210.01495, to appear in Journal de Théorie des Nombres de Bordeaux.

  9. The Batyrev-Manin conjecture for DM stacks,
    joint work with Ratko Darda,
    Journal of the European Mathematical Society, published online first, (Jul. 2024). DOI:https://doi.org/10.4171/jems/1510

  10. Torsors for finite group schemes of bounded height,
    joint work with Ratko Darda,
    Journal of London Mathematical Society, Vol. 108, Issue 3, 1275-1331, (Sep. 2023). DOI:https://doi.org/10.1112/jlms.12780

  11. The isomorphism problem of projective schemes and related algorithmic problems,
    International Journal of Algebra and Computation, Vol. 33, No. 5, 893-926, (Jun. 2023). DOI:https://doi.org/10.1142/S021819672350039X

  12. Open problems in the wild McKay correspondence and related fields,
    Advanced Studies in Pure Mathematics, Vol. 88 "McKay correspondence, Mutation and related topics," 279-303, (Apr. 2023). DOI:https://doi.org/10.2969/aspm/08810279

  13. On the behavior of stringy motives under Galois quasi-étale covers,
    joint work with Javier Carvajal-Rojas,
    arXiv:2105.05214.

  14. The wild McKay correspondence for cyclic groups of prime power order,
    joint work with Mahito Tanno,
    Illinois Journal os Mathematics, 65, 619-654, (Sep. 2021). DOI:https://doi.org/10.1215/00192082-9402078

  15. Moduli of formal torsors II,
    joint work with Fabio Tonini,
    Annales l'Institut Fourier, Vo. 73, No. 2, 511-558, (May 2023). DOI:https://doi.org/10.5802/aif.3533

  16. Motivic integration over wild Deligne-Mumford stacks,
    Algebraic Geometry, 11(2), 178–255, (Mar. 2024). DOI:https://doi.org/10.14231/AG-2024-007

  17. The wild McKay correspondence via motivic integration,
    Sugaku, 70, 159-183 (Apr. 2018)
    (in Japanese. The original Japanese title is モチーフ積分による野性マッカイ対応.)
    DOI:https://doi.org/10.11429/sugaku.0702159, English version in Sugaku Expositions

  18. Notes on the motivic McKay correspondence for the group scheme \(\alpha_p \),
    joint work with Fabio Tonini,
    Singularities — Kagoshima 2017; Proceedings of the 5th Franco-Japanese-Vietnamese Symposium on Singularities, 215-233 (Jul. 2020). DOI:https://doi.org/10.1142/9789811206030_0011

  19. Discrepancies of \(p\)-cyclic quotient varieties,
    Journal of Mathematical Sciences, the University of Tokyo, 26, 1-14 (Mar. 2019). Journal article page

  20. Moduli of formal torsors,
    joint work with Fabio Tonini,
    Journal of Algebraic Geometry, 29, 753-801 (Jun. 2020). DOI:https://doi.org/10.1090/jag/771

  21. Motivic Serre invariants modulo the square of \(\mathbb{L}-1\),
    Proceedings of the American Mathematical Society, 146, 547-554 (Feb. 2018). DOI:https://doi.org/10.1090/proc/13780

  22. Vojta’s conjecture, singularities and multiplier-type ideals,
    Kodai Mathematical Journal, 41, 566-578 (Oct. 2018).
    DOI:https://doi.org/10.2996/kmj/1540951254 (this is a shortened version of the preprint "Vojta's conjecture for singular varieties", arXiv:1610.03593).

  23. Mass formulas for local Galois representations and quotient singularities II: dualities and resolution of singularities,
    joint work with Melanie Matchett Wood
    Algebra & Number Theory, 11, 817-840 (Jun. 2017).
    DOI:https://doi.org/10.2140/ant.2017.11.817 (Errata to this paper is to appear on the ANT website. Here are supplementary notes.)

  24. Manin's conjecture vs. Malle's conjecture,
    arXiv:1505.04555.

  25. The wild McKay correspondence and \(p\)-adic measures,
    Journal of the European Mathematical Society, 19, 3709-3734 (Nov. 2017). DOI:https://doi.org/10.4171/jems/751

  26. Densities of rational points and number fields,
    arXiv:1408.3912.

  27. Wilder McKay correspondences,
    Nagoya Mathematical Journal, 221, 111-164 (Mar. 2016). DOI:https://doi.org/10.1017/nmj.2016.3

  28. Mass formulas for local Galois representations and quotient singularities I: a comparison of counting functions,
    joint work with Melanie Matchett Wood,
    International Mathematics Research Notices, 2015, 12590–12619 (Jan. 2015).
    DOI:https://doi.org/10.1093/imrn/rnv074

  29. Toward motivic integration over wild Deligne-Mumford stacks,
    Higher dimensional algebraic geometry, Advanced Studies in Pure Mathematics, 74, 407-437 (2017). DOI:https://doi.org/10.2969/aspm/07410407

  30. Higher Semple-Nash blowups and F-blowups,
    Clay Mathematics Proceedings, Vol. 20, 327-340 (Jan., 2014). PDF of the entire volueme

  31. The p-cyclic McKay correspondence via motivic integration,
    Compositio Mathematica, 150, 1125-1168 (Jul., 2014).
    DOI:https://doi.org/10.1112/S0010437X13007781

  32. Pure subrings of regular local rings, endomorphism rings and Frobenius morphisms,
    Journal of Algebra, 370, 15-31 (Nov., 2012).
    DOI:https://doi.org/10.1016/j.jalgebra.2012.07.027

  33. F-blowups of normal surface singularities,
    joint work with Nobuo Hara and Tadakazu Sawada,
    Algebra & Number Theory 7-3, 733--763 (Aug., 2013).
    DOI:http://dx.doi.org/10.2140/ant.2013.7.733

  34. Frobenius morphisms of noncommutative blowups,
    Singularities in Geometry and Topology, Strasbourg 2009 (IRMA Lectures in Mathematics and Theoretical Physics 20), 269-283 (Dec., 2012). DOI:https://doi.org/10.4171/118-1/14

  35. Universal flattening of Frobenius,
    American Journal of Mathematics, 134, 349-378 (Apr., 2012).
    DOI:https://doi.org/10.1353/ajm.2012.0014, JSTOR article page

  36. Noncommutative resolution, F-blowups and D-modules,
    joint work with Yukinobu Toda,
    Advances in Mathematics, 222, 318-330 (Sep., 2009).
    DOI:https://doi.org/10.1016/j.aim.2009.04.004

  37. On monotonicity of F-blowup sequences,
    Illinois Journal of Mathematics, 53, 101-110 (May, 2009). DOI:https://doi.org/10.1215/ijm/1264170841

  38. Non-adic formal schemes,
    International Mathematics Research Notices, 2009, 2417-2475 (Feb., 2009).
    DOI:https://doi.org/10.1093/imrn/rnp021

  39. Flag higher Nash blowups,
    Communications in Algebra, 37, 1001-1015 (Mar., 2009).
    DOI:https://doi.org/10.1080/00927870802279022

  40. Higher Nash blowups,
    Compositio Mathematica, 143, 1493-1510 (Nov., 2007). DOI:https://doi.org/10.1112/S0010437X0700276X

  41. Motivic integration over Deligne-Mumford stacks,
    Advances in Mathematics, 207, 707-761 (Dec., 2006).
    DOI:https://doi.org/10.1016/j.aim.2006.01.004

  42. Jet schemes, log discrepancies and inversion of adjunction,
    joint work with L. Ein and M. Mustata,
    Inventiones Mathematicae, 153, 519-535, (Sep., 2003). DOI:https://doi.org/10.1007/s00222-003-0298-3

  43. Dimensions of jet schemes of log singularities,
    American Journal of Mathematics, 125, 1137-1145 (Oct., 2003). DOI:https://doi.org/10.1353/ajm.2003.0037, JSTOR article page

  44. Twisted jets, motivic measures and orbifold cohomology,
    Compositio Mathematica, 140, 396-422 (Mar., 2004).　 DOI:https://doi.org/10.1112/S0010437X03000368

Last update: November 11, 2024