Books
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Motivic integration, the McKay correspondence and wild ramification, in preparation, version:2021-11-11.
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A Glimpse into University Math Through Games, Kyoritsu Shuppan (Dec. 2018).
Papers
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The Manin conjecture for toric stacks,
joint work with Ratko Darda,
arXiv:2311.02012. -
Higher Jacobian ideals, contact equivalence and motivic zeta functions,
joint work with Quy Thuong Lê,
arXiv:2310.07976. -
Non-commutative resolutions of linearly reductive quotient singularities,
joint work with Christian Liedtke,
arXiv:2304.14711. -
F-blowups and essential divisors for toric varieties,
joint work with Enrique Chávez-Martínez and Daniel Duarte,
arXiv:2304.13247. -
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,
arXiv:2302.08376, to appear in the proceedings of the conference "Recent Advances and New Directions in the Interplay of Noncommutative Algebra and Geometry," a Conference in honor of S. Paul Smith on the occasion of his 65th birthday. -
Quantitative inverse Galois problem for semicommutative finite group schemes,
joint work with Ratko Darda,
arXiv:2210.01495. -
The Batyrev-Manin conjecture for DM stacks,
joint work with Ratko Darda,
arXiv:2207.03645, to appear in the Journal of the European Mathematical Society. -
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). -
The isomorphism problem of projective schemes and related algorithmic problems,
International Journal of Algebra and Computation, Vol. 33, No. 5, 893-926, (Jun. 2023). -
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). -
On the behavior of stringy motives under Galois quasi-étale covers,
joint work with Javier Carvajal-Rojas,
arXiv:2105.05214. -
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). -
Moduli of formal torsors II,
joint work with Fabio Tonini,
Annales l'Institut Fourier, Vo. 73, No. 2, 511-558, (May 2023). -
Motivic integration over wild Deligne-Mumford stacks,
Algebraic Geometry, 11(2), 178–255, (Mar. 2024). -
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.) -
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). -
Discrepancies of \(p\)-cyclic quotient varieties,
Journal of Mathematical Sciences, the University of Tokyo, 26, 1-14 (Mar. 2019). -
Moduli of formal torsors,
joint work with Fabio Tonini,
Journal of Algebraic Geometry, 29, 753-801 (Jun. 2020). -
Motivic Serre invariants modulo the square of \(\mathbb{L}-1\),
Proceedings of the American Mathematical Society, 146, 547-554 (Feb. 2018). -
Vojta’s conjecture, singularities and multiplier-type ideals,
Kodai Mathematical Journal, 41, 566-578 (Oct. 2018).
(this is a shortened version of the preprint "Vojta's conjecture for singular varieties", arXiv:1610.03593). -
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).
(Errata to this paper is to appear on the ANT website. Here are supplementary notes.) -
Manin's conjecture vs. Malle's conjecture,
arXiv:1505.04555. -
The wild McKay correspondence and \(p\)-adic measures,
Journal of the European Mathematical Society, 19, 3709-3734 (Nov. 2017). -
Densities of rational points and number fields,
arXiv:1408.3912. -
Wilder McKay correspondences,
Nagoya Mathematical Journal, 221, 111-164 (Mar. 2016). -
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). -
Toward motivic integration over wild Deligne-Mumford stacks,
Higher dimensional algebraic geometry, Advanced Studies in Pure Mathematics, 74, 407-437 (2017). -
Higher Semple-Nash blowups and F-blowups,
Clay Mathematics Proceedings, Vol. 20, 327-340 (Jan., 2014). -
The p-cyclic McKay correspondence via motivic integration,
Compositio Mathematica, 150, 1125-1168 (Jul., 2014). -
Pure subrings of regular local rings, endomorphism rings and Frobenius morphisms,
Journal of Algebra, 370, 15-31 (Nov., 2012). -
F-blowups of normal surface singularities,
joint work with Nobuo Hara and Tadakazu Sawada,
Algebra & Number Theory 7-3, 733--763 (Aug., 2013). -
Frobenius morphisms of noncommutative blowups,
Singularities in Geometry and Topology, Strasbourg 2009 (IRMA Lectures in Mathematics and Theoretical Physics 20), 269-283 (Dec., 2012). -
Universal flattening of Frobenius,
American Journal of Mathematics, 134, 349-378 (Apr., 2012). -
Noncommutative resolution, F-blowups and D-modules,
joint work with Yukinobu Toda,
Advances in Mathematics, 222, 318-330 (Sep., 2009). -
On monotonicity of F-blowup sequences,
Illinois Journal of Mathematics, 53, 101-110 (May, 2009). -
Non-adic formal schemes,
International Mathematics Research Notices, 2009, 2417-2475 (Feb., 2009). -
Flag higher Nash blowups,
Communications in Algebra, 37, 1001-1015 (Mar., 2009). -
Higher Nash blowups,
Compositio Mathematica, 143, 1493-1510 (Nov., 2007). -
Motivic integration over Deligne-Mumford stacks,
Advances in Mathematics, 207, 707-761 (Dec., 2006). -
Jet schemes, log discrepancies and inversion of adjunction,
joint work with L. Ein and M. Mustata,
Inventiones Mathematicae, 153, 519-535, (Sep., 2003). -
Dimensions of jet schemes of log singularities,
American Journal of Mathematics, 125, 1137-1145 (Oct., 2003). -
Twisted jets, motivic measures and orbifold cohomology,
Compositio Mathematica, 140, 396-422 (Mar., 2004).