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• On the semi-infinite Deligne–Lusztig varieties for $$\textrm{GSp}$$
  Teppei Takamatsu
  manuscripta mathematica, Volume：176, Number：6, Dec. 2025, [Reviewed]
  Abstract
  
  We prove that Lusztig’s semi-infinite Deligne–Lusztig variety for $$\textrm{GSp}$$ (and its inner form) is isomorphic, as a set with action, to an affine Deligne–Lusztig variety at infinite level, generalizing a result of Chan–Ivanov. Furthermore, we show that a component of some affine Deligne–Lusztig variety $$X^0_{w_r}(b)_{\mathcal {L } }$$ for $$\textrm{GSp}$$ can be written, up to perfection, as a direct product of a classical Deligne–Lusztig variety with an affine space. We also study the varieties $$X_h$$ defined by Chan and Ivanov, and show that $$X_h$$ at infinite level can be realized as a subset of semi-infinite Deligne–Lusztig varieties defined using components of affine Deligne–Lusztig varieties such as $$X^0_{w_r}(b)_{\mathcal {L } }$$ above, even in the $$\textrm{GSp}$$ case. This reinterprets previous constructions of representations from $$X_h$$ as instances of Lusztig’s conjectural picture.
  Springer Science and Business Media LLC, Scientific journal
  DOI：https://doi.org/10.1007/s00229-025-01674-3
  DOI ID：10.1007/s00229-025-01674-3, ISSN：0025-2611, eISSN：1432-1785
• Quasi-F-splittings in birational geometry　　　　　　　　　　　　　　　
  Tatsuro KAWAKAMI; Teppei TAKAMATSU; Hiromu TANAKA; Jakub WITASZEK; Fuetaro YOBUKO; Shou YOSHIKAWA
  Annales Scientifiques de l'École Normale Supérieure, Sep. 2025, [Reviewed]
  Societe Mathematique de France, Scientific journal
  DOI：https://doi.org/10.24033/asens.2614
  DOI ID：10.24033/asens.2614, ISSN：0012-9593, eISSN：1873-2151
• Reduction of bielliptic surfaces
  Teppei Takamatsu
  Canadian Mathematical Bulletin, First page：1, Last page：18, Feb. 2025, [Reviewed]
  Abstract
  
  A bielliptic surface (or hyperelliptic surface) is a smooth surface with a numerically trivial canonical divisor such that the Albanese morphism is an elliptic fibration. In the first part of this article, we study the structure of bielliptic surfaces over a field of characteristic different from $2$ and $3$ , in order to prove the Shafarevich conjecture for bielliptic surfaces with rational points. Furthermore, we demonstrate that the Shafarevich conjecture does not generally hold for bielliptic surfaces without rational points. In particular, this article completes the study of the Shafarevich conjecture for minimal surfaces of Kodaira dimension $0$ . In the second part of this article, we study a Néron model of a bielliptic surface. We establish the potential existence of a Néron model for a bielliptic surface when the residual characteristic is not equal to $2$ or $3$ .
  Canadian Mathematical Society, Scientific journal
  DOI：https://doi.org/10.4153/s0008439525000153
  DOI ID：10.4153/s0008439525000153, ISSN：0008-4395, eISSN：1496-4287
• On the finiteness of twists of irreducible symplectic varieties
  Teppei Takamatsu
  Mathematische Annalen, Volume：392, Number：1, First page：339, Last page：371, Feb. 2025, [Reviewed]
  Abstract
  
  Irreducible symplectic varieties are higher-dimensional analogues of K3 surfaces. In this paper, we prove the finiteness of twists of irreducible symplectic varieties for a fixed finite field extension of characteristic 0. The main ingredient of the proof is the cone conjecture for irreducible symplectic varieties, which was proved by Markman and Amerik–Verbitsky. As byproducts, we also discuss the cone conjecture over non-closed fields by Bright–Logan–van Luijk’s method. We also give an application to the finiteness of derived equivalent twists. Moreover, we discuss the case of K3 surfaces or Enriques surfaces over fields of positive characteristic.
  Springer Science and Business Media LLC, Scientific journal
  DOI：https://doi.org/10.1007/s00208-025-03090-0
  DOI ID：10.1007/s00208-025-03090-0, ISSN：0025-5831, eISSN：1432-1807
• Quasi-F-splittings in birational geometry II　　　　　　　　　　　　　　　
  Tatsuro Kawakami; Teppei Takamatsu; Hiromu Tanaka; Jakub Witaszek; Fuetaro Yobuko; Shou Yoshikawa
  Proceedings of the London Mathematical Society, Volume：128, Number：4, Aug. 2024, [Reviewed]
  Abstract
  
  Over an algebraically closed field of characteristic , we prove that three‐dimensional ‐factorial affine klt varieties are quasi‐‐split. Furthermore, we show that the bound on the characteristic is optimal.
  Wiley
  DOI：https://doi.org/10.1112/plms.12593
  DOI ID：10.1112/plms.12593, ISSN：0024-6115, eISSN：1460-244X, arXiv ID：arXiv:2408.01921
• On behavior of conductors, Picard schemes, and Jacobian numbers of varieties over imperfect fields　　　　　　　　　　　　　　　
  Ippei Nagamachi; Teppei Takamatsu
  Journal of Pure and Applied Algebra, Volume：228, Number：4, First page：107501, Last page：107501, Apr. 2024, [Reviewed]
  Elsevier BV, Scientific journal
  DOI：https://doi.org/10.1016/j.jpaa.2023.107501
  DOI ID：10.1016/j.jpaa.2023.107501, ISSN：0022-4049
• Minimal model program for semi-stable threefolds in mixed characteristic　　　　　　　　　　　　　　　
  Teppei Takamatsu; Shou Yoshikawa
  Journal of Algebraic Geometry, Volume：32, Number：3, First page：429, Last page：476, Mar. 2023, [Reviewed]
  

  In this paper, we study the minimal model theory for threefolds in mixed characteristic. As a generalization of a result of Kawamata, we show that the minimal model program (MMP) holds for strictly semi-stable schemes over an excellent Dedekind scheme of relative dimension two without any assumption on the residue characteristics of . We also prove that we can run a -MMP over , where is a projective birational morphism of -factorial quasi-projective -schemes and is a three-dimensional dlt pair with .

  
  American Mathematical Society (AMS), Scientific journal
  DOI：https://doi.org/10.1090/jag/813
  DOI ID：10.1090/jag/813, ISSN：1056-3911, eISSN：1534-7486
• The Shafarevich conjecture and some extension theorems for proper hyperbolic polycurves　　　　　　　　　　　　　　　
  Ippei Nagamachi; Teppei Takamatsu
  Mathematical Research Letters, Volume：29, Number：2, First page：541, Last page：558, 2022, [Reviewed]
  International Press of Boston, Scientific journal
  DOI：https://doi.org/10.4310/mrl.2022.v29.n2.a10
  DOI ID：10.4310/mrl.2022.v29.n2.a10, ISSN：1073-2780, eISSN：1945-001X
• On a cohomological generalization of the Shafarevich conjecture for K3 surfaces
  Teppei Takamatsu
  Algebra & Number Theory, Volume：14, Number：9, First page：2505, Last page：2531, Oct. 2020, [Reviewed]
  Mathematical Sciences Publishers, Scientific journal
  DOI：https://doi.org/10.2140/ant.2020.14.2505
  DOI ID：10.2140/ant.2020.14.2505, ISSN：1937-0652, eISSN：1944-7833
• On the Shafarevich conjecture for Enriques surfaces
  Teppei Takamatsu
  Mathematische Zeitschrift, Volume：298, Number：1-2, First page：489, Last page：495, Sep. 2020, [Reviewed]
  Springer Science and Business Media LLC, Scientific journal
  DOI：https://doi.org/10.1007/s00209-020-02623-4
  DOI ID：10.1007/s00209-020-02623-4, ISSN：0025-5874, eISSN：1432-1823

• Non-quasi-$F$-split canonical affine fourfolds exist in every characteristic
  Teppei Takamatsu; Shou Yoshikawa
  16 Feb. 2026
  We construct canonical $\mathbb{Q}$-factorial Gorenstein affine fourfolds in every positive characteristic that are not quasi-$F$-split.
  arXiv ID：arXiv:2602.14792
• Fano threefolds of genus 12 with large automorphism group in positive and mixed characteristic
  Tetsushi Ito; Akihiro Kanemitsu; Teppei Takamatsu; Yuuji Tanaka
  15 Jan. 2026
  We study prime Fano threefolds of genus 12 ($V_{22}$-varieties) with positive-dimensional automorphism groups in positive and mixed characteristic. We classify such varieties over any perfect field. In particular, we prove that $V_{22}$-varieties of Mukai-Umemura type over $k$ exist if and only if $\mathrm{char}\ k \neq 2$, $5$. We also prove the same result for $\mathbb{G}_a$-type. As arithmetic applications, we show that the Shafarevich conjecture holds for $V_{22}$-varieties of Mukai-Umemura type and of $\mathbb{G}_m$-type, while it fails for $V_{22}$-varieties of $\mathbb{G}_a$-type. Moreover, we prove that there exists $V_{22}$-varieties over $\mathbb{Z}$, whereas there do not exist $V_{22}$-varieties over $\mathbb{Z}$ whose generic fiber has a positive-dimensional automorphism group.
  arXiv ID：arXiv:2601.10106
• Quasi-$F^{\infty}$-split height versus quasi-$F$-regular height for rational double points and graded rings
  Teppei Takamatsu; Shou Yoshikawa
  07 Jan. 2026
  In this paper, we study a phenomenon concerning quasi-$F$-singularities: under suitable hypotheses, the finiteness of the quasi-$F^{\infty}$-split height ($\mathrm{ht}^{\infty}$) implies quasi-$F$-regularity, and moreover, $\mathrm{ht}^{\infty}$ coincides with the quasi-$F$-regular height ($\mathrm{ht}^{\mathrm{reg } }$). We establish this coincidence for two important classes of isolated Gorenstein singularities. First, we explicitly compute $\mathrm{ht}^{\infty}$ and $\mathrm{ht}^{\mathrm{reg } }$ for all rational double points, showing that every non-$F$-pure rational double point satisfies $\mathrm{ht}^\infty = \mathrm{ht}^{\mathrm{reg } }$. Second, for localizations of graded non-$F$-pure normal Gorenstein rings with $F$-rational punctured spectrum, we again obtain the equality $\mathrm{ht}^\infty = \mathrm{ht}^{\mathrm{reg } }$.
  arXiv ID：arXiv:2601.03491
• Fedder type criteria for quasi-$F$-splitting II
  Tatsuro Kawakami; Teppei Takamatsu; Shou Yoshikawa
  21 Nov. 2025
  In this paper, we apply Fedder-type criteria for quasi-$F$-splitting to provide explicit computations of quasi-$F$-split heights for Calabi-Yau hypersurfaces, bielliptic surfaces, Fano varieties, and rational double points. We also find interesting phenomena concerned with inversion of adjunction, fiber products, Fano varieties, and general fibers of fibrations.
  arXiv ID：arXiv:2511.17270
• Quasi-$F$-splitting and smooth weak del Pezzo surfaces in mixed characteristic
  Hirotaka Onuki; Teppei Takamatsu; Shou Yoshikawa
  22 Oct. 2025
  We introduce the notion of quasi-$F$-splitting in mixed characteristic and study Kodaira-type vanishing on quasi-$F$-splitting varieties. As an application, we prove a Kodaira-type vanishing on lifts of rational double point (RDP) del Pezzo surfaces.
  arXiv ID：arXiv:2510.19308
• Arithmetic monodromy of hyper-Kähler varieties over $p$-adic fields
  Kazuhiro Ito; Tetsushi Ito; Teruhisa Koshikawa; Teppei Takamatsu; Haitao Zou
  18 Jul. 2025
  In this paper, we study the $p$-adic and $\ell$-adic monodromy operators associated with hyper-Kähler varieties over $p$-adic fields, in connection with Looijenga-Lunts-Verbitsky Lie algebras. We investigate a conjectural relation between the nilpotency indices of these monodromy operators on higher-degree cohomology groups and on the second cohomology, which may be viewed as an arithmetic analogue of Nagai's conjecture for degenerations of hyper-Kähler manifolds over a disk. We verify this arithmetic version of Nagai's conjecture for hyper-Kähler varieties over $p$-adic fields, assuming they belong to one of the four known deformation types. As part of our approach, we introduce a new method to analyze the $p$-adic cohomology of hyper-Kähler varieties via Sen's theory.
  arXiv ID：arXiv:2507.13713
• Quintic del Pezzo threefolds in positive and mixed characteristic
  Tetsushi Ito; Akihiro Kanemitsu; Teppei Takamatsu; Yuuji Tanaka
  18 Jun. 2025
  We show that smooth quintic del Pezzo threefolds over arbitrary base schemes are classified by non-degenerate ternary symmetric bilinear forms. Then we describe the automorphism group schemes, the Hilbert schemes of lines and the orbit structures of quintic del Pezzo threefolds, and we find several new phenomena in characteristic two. As arithmetic applications, we prove a refinement of the Shafarevich conjecture, and prove that there are exactly two isomorphism classes of quintic del Pezzo threefolds over the ring of rational integers.
  arXiv ID：arXiv:2506.15086
• Finiteness of pointed families of symplectic varieties: a geometric Shafarevich conjecture
  Lie Fu; Zhiyuan Li; Teppei Takamatsu; Haitao Zou
  21 May 2025
  We investigate in this paper the so-called pointed Shafarevich problem for families of primitive symplectic varieties. More precisely, for any fixed pointed curve $(B, 0)$ and any fixed primitive symplectic variety $X$, among all locally trivial families of $\mathbb{Q}$-factorial and terminal primitive symplectic varieties over $B$ whose fiber over $0$ is isomorphic to $X$, we show that there are only finitely many isomorphism classes of generic fibers. Moreover, assuming semi-ampleness of isotropic nef divisors, which holds true for all hyper-Kähler manifolds of known deformation types, we show that there are only finitely many such projective families up to isomorphism. These results are optimal since we can construct infinitely many pairwise non-isomorphic (not necessarily projective) families of smooth hyper-Kähler varieties over some pointed curve $(B, 0)$ such that they are all isomorphic over the punctured curve $B\backslash \{0\}$ and have isomorphic fibers over the base point $0$.
  arXiv ID：arXiv:2505.15295
• Arithmetic finiteness of Mukai varieties of genus 7
  Tetsushi Ito; Akihiro Kanemitsu; Teppei Takamatsu; Yuuji Tanaka
  30 Sep. 2024
  We study arithmetic finiteness of prime Fano threefolds of genus 7 and their higher dimensional generalization, called Mukai varieties of genus 7. For prime Fano threefolds of genus 7, we provide an arithmetic refinement of the Torelli theorem, obtain Shafarevich-type finiteness results, and show the failure of the Néron--Ogg--Shafarevich criterion of good reduction. For Mukai varieties of genus 7, we prove that Shafarevich-type finiteness results hold in dimensions 9 and 10, but fail in dimension 6. In addition, we show that Mukai $n$-folds of genus 7 over $\mathbb{Z}$ do not exist for $n \leq 4$, whereas they exist for $5 \leq n \leq 10$.
  arXiv ID：arXiv:2409.20046
• Quasi-F-splittings in birational geometry III
  Tatsuro Kawakami; Teppei Takamatsu; Hiromu Tanaka; Jakub Witaszek; Fuetaro Yobuko; Shou Yoshikawa
  04 Aug. 2024
  We prove that $\mathbb Q$-Gorenstein quasi-$F$-regular singularities are klt. To this end, we shall introduce quasi-test ideals.
  arXiv ID：arXiv:2408.01921
• On the supersingular locus of the Siegel modular variety of genus 3 or 4
  Ryosuke Shimada; Teppei Takamatsu
  28 Mar. 2024
  We study the supersingular locus of the Siegel modular variety of genus 3 or 4. More concretely, we decompose the supersingular locus into a disjoint union of the product of a Deligne-Lusztig variety of Coxeter type and a finite-dimensional affine space after taking perfection.
  arXiv ID：arXiv:2403.19505
• On Frobenius liftability of surface singularities
  Tatsuro Kawakami; Teppei Takamatsu
  13 Feb. 2024
  We show that a plt surface singularity $(P\in X,B)$ is $F$-liftable if and only if it is $F$-pure and is not a rational double point of type $E_8^1$ in characteristic $p=5$. As a consequence, we prove the logarithmic extension theorem for $F$-pure surface pairs and Bogomolov-Sommese vanishing for globally $F$-split surface pairs. These results were previously known to hold in characteristic $p>5$.
  arXiv ID：arXiv:2402.08152
• Fedder type criteria for quasi-$F$-splitting I
  Tatsuro Kawakami; Teppei Takamatsu; Shou Yoshikawa
  21 Apr. 2022
  Yobuko recently introduced the notion of quasi-$F$-splitting and quasi-$F$-split heights, which generalize and quantify the notion of Frobenius-splitting, and proved that quasi-$F$-split heights coincide with Artin-Mazur heights for Calabi-Yau varieties. In this paper, we prove Fedder type criteria for quasi-$F$-splittings of complete intersections, and in particular, obtain a simple formula to compute Artin-Mazur heights of Calabi-Yau hypersurfaces. As one of its applications, we prove that there exist Calabi-Yau varieties of arbitrarily high Artin-Mazur height over $\mathbb{F}_2$. We also give explicit defining equations of quartic K3 surfaces over $\mathbb{F}_{3}$ realizing all the possible Artin-Mazur heights.
  arXiv ID：arXiv:2204.10076
• Unpolarized Shafarevich conjectures for hyper-Kähler varieties
  Lie Fu; Zhiyuan Li; Teppei Takamatsu; Haitao Zou
  19 Mar. 2022
  The Shafarevich conjecture/problem is about the finiteness of isomorphism classes of a family of varieties defined over a number field with good reduction outside a finite collection of places. For K3 surfaces, such a finiteness result was proved by Y. She. For hyper-Kähler varieties, which are higher-dimensional analogs of K3 surfaces, Y. André proved the Shafarevich conjecture for hyper-Kähler varieties of a given dimension and admitting a very ample polarization of bounded degree. In this paper, we provide a unification of both results by proving the (unpolarized) Shafarevich conjecture for hyper-Kähler varieties in a given deformation type. We also discuss the cohomological generalization of the Shafarevich conjecture by replacing the good reduction condition by the unramifiedness of the cohomology, where our results are subject to a certain necessary assumption on the faithfulness of the action of the automorphism group on cohomology. In a similar fashion, generalizing a result of Orr and Skorobogatov on K3 surfaces, we prove the finiteness of geometric isomorphism classes of hyper-Kähler varieties of CM type in a given deformation type defined over a number field with bounded degree. A key to our approach to these results is a uniform Kuga--Satake map, inspired by She's work, and we study its arithmetic properties, which are of independent interest.
  arXiv ID：arXiv:2203.10391

• May 2021 - Present