The isomorphism problem of projective schemes and related algorithmic problems,
arXiv:2107.09277
Open problems in the wild McKay correspondence and related fields,
arXiv:2107.07073
On the behavior of stringy motives under Galois quasi-étale covers,
joint work with Javier Carvajal-Rojas,
arXiv:arXiv:2105.05214.
The wild McKay correspondence for cyclic groups of prime power order,
joint work with Mahito Tanno,
arXiv:2006.12048, to appear in Illinois Journal os Mathematics.
Moduli of formal torsors II,
joint work with Fabio Tonini,
arXiv:1909.09276, to appear in Annales l'Institut Fourier.
Motivic integration over wild Deligne-Mumford stacks,
arXiv:1908.02932.
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).