Basic Information

Affiliated programs (koza)

• Graduate School of Science, 数学・数理解析専攻 解析数理講座, 助教

Professional Memberships

• 日本数学会

Academic Degree

• M.S.(The University of Chicago)
• Ph.D.(The University of Chicago)

ID,URL

• J-Global ID

  201601012565185340

researchmap URL

• https://researchmap.jp/7000017226

Research

Research Topics, Overview of the research

• Research Topics

  Motives(cohomology of algebraic varieties). In particular, p-adic Hodge theory, Shimura varieties, K3 surfaces.

• Overview of the research

  I have been studying cohomology of algebraic varieties, particularly, so-called pure motives. My works include study of heights of motives, p-adic Hodge thoery, the Tate conjecture for products of K3 surfaces, and cohomology of Shimura varieties. I'm also interested in the Langlands programme, which connects automorphic representations and pure motives.

Research Areas

• Natural sciences, Algebra

Papers

• The Hodge standard conjecture for self-products of K3 surfaces

  Kazuhiro Ito; Tetsushi Ito; Teruhisa Koshikawa

  Journal of Algebraic Geometry, 03 Oct. 2024

  
• The numerical Hodge standard conjecture for the square of a simple abelian variety of prime dimension

  Teruhisa Koshikawa

  manuscripta mathematica, 13 May 2023

  
• CM liftings of surfaces over finite fields and their applications to the Tate conjecture

  Kazuhiro Ito; Tetsushi Ito; Teruhisa Koshikawa

  Forum of Mathematics, Sigma, Apr. 2021, Peer-reviewed

  Access this paper :

  
• Vanishing theorems for the mod p cohomology of some simple Shimura varieties

  Teruhisa Koshikawa

  Forum of Mathematics, Sigma, Nov. 2020, Peer-reviewed

  
• The Ainf-cohomology in the semistable case

  Kestutis Cesnavicius; Teruhisa Koshikawa

  Compositio Mathematica, Nov. 2019, Peer-reviewed

  
• Overconvergent unit-root F-isocrystals and isotriviality

  Teruhisa Koshikawa

  Mathematical Research Letters, Jan. 2018, Peer-reviewed

  

Misc.

• On the non-generic part of the L2-cohomology of locally symmetric spaces

  Teruhisa Koshikawa; Sug Woo Shin

  Feb. 2025

  
• A-parameters and eigensheaves

  Teruhisa Koshikawa

  Arithmetic Geometry, Oberwolfach Reports, Nov. 2024, Invited

  
• Inequalities characterizing distinguished unipotent orbits

  Alexander Bertoloni Meli; Teruhisa Koshikawa; Jonathan Leake

  09 Sep. 2024

  
• Logarithmic prismatic cohomology II

  Teruhisa Koshikawa; Zijian Yao

  01 Jun. 2023

  
• Genericity and cohomology of locally symmetric spaces

  Teruhisa Koshikawa

  Arithmetic of Shimura varieties, Oberwolfach Reports, Mar. 2023, Invited

  
• Relative $A_{\rm inf}$-cohomology

  Ildar Gaisin; Teruhisa Koshikawa

  16 Jun. 2022

  
• 書評 Laurent Fargues and Jean-Marc Fontaine : Courbes et Fibres Vectoriels en Theorie de Hodge p-adique, Asterisque, 406, Soc. Math. France, 2018年, ⅹⅲ+382ページ

  越川皓永

  数学, 2021, Peer-reviewed, Invited

  
• On the generic part of the cohomology of local and global Shimura varieties

  Teruhisa Koshikawa

  20 Jun. 2021

  
• Eichler-Shimura relations for local Shimura varieties

  Teruhisa Koshikawa

  20 Jun. 2021

  
• Logarithmic Prismatic Cohomology I

  Teruhisa Koshikawa

  28 Jul. 2020

  
• Galois representations associated with a non-selfdual automorphic representation of GL(3)

  Tetsushi Ito; Teruhisa Koshikawa; Yoichi Mieda

  28 Nov. 2018

  
• 半安定還元の場合の Ainf コホモロジー

  越川 皓永

  代数学シンポジウム報告集, 2018, Invited

  
• On heights of motives with semistable reduction

  Teruhisa Koshikawa

  08 May 2015

  

Presentations

• On the spectral side of the categorical local Langlands

  Automorphic Forms and Arithmetic, 14 Mar. 2025, Invited

  
• A-parameters, eigensheaves, and cuspidal coherent sheaves

  Geometric Approaches to the Local Langlands Program, Invited

  
• Cohomology of log prismatic F-crystals

  Arithmetic Geometry in Shenzhen, 18 Dec. 2024, Invited

  
• Cohomology of log prismatic F-crystals

  Workshop on p-adic Geometry, 20 Nov. 2024, Invited

  
• A-parameters and eigensheaves

  p-adic Methods in Number Theory and Arithmetic Geometry, 11 Nov. 2024, Invited

  
• Cohomology of log prismatic F-crystals

  L-fucntions and Motives in Niseko 2024, 18 Sep. 2024, Invited

  
• A-parameters and eigensheaves

  Arithmetic geometry, Oberwolfach worksop, 17 Jul. 2024, Invited

  
• Around the categorical local Langlands

  National University of Singapore Seminars :Representation Theory and Number Theory, 18 Apr. 2024, Invited

  
• A-parameters and eigensheaves

  2024 Clay Research Workshop, New Advances in the Langlands Program: Geometry and Arithmetic, Invited

  
• Spectral side of categorical local Langlands

  Summer school on Galois representations and reciprocity, 07 Jul. 2024, Invited

  
• 志村多様体のコホモロジーの消滅定理

  日本数学会2024年度年会, 18 Mar. 2024, Invited

  
• Some computations in categorical local Langlands

  Arithmetic and Cohomology of Algebraic Varieties 2023, 21 Sep. 2023, Invited

  
• Vanishing range beyond the generic case

  Trimester Program, The Arithmetic of the Langlands Program, Trimester Seminar Series, 17 Aug. 2023, Invited

  
• Around logarithmic primsatic cohomology

  Teruhisa Koshikawa

  IAS/Princeton Arithmetic Geometry Seminar, 10 Apr. 2023, Invited

  
• Genericity and cohomology of locally symmetric spaces

  Arithmetic of Shimura varieties, Oberwolfach workshop, 30 Jan. 2023, Invited

  
• On the generic part of the cohomology of locally symmetric spaces

  Mini-workshop on the geometrization of the local Langlands correspondences and related topics, 22 Dec. 2022, Invited

  
• Logarithmic prismatic cohomology

  p-adic cohomology and arithmetic geometry 2022, 07 Nov. 2022, Invited

  
• K3曲面の自己積のHodge標準予想

  北海道大学数論セミナー, 27 Oct. 2022

  
• On the cohomology of unitary Shimura varieties

  Community-building in the Langlands Program, 16 Aug. 2022, Invited

  
• Some cases of the Hodge standard conjecture

  Franco-Asian Summer School on Arithmetic Geometry, 02 Jun. 2022, Invited

  
• Vanishing theorems for local ang global Shimura varieties

  30eradecaen : 30e Rencontres arithmétiques de Caen, 26 May 2022, Invited

  
• ユニタリ志村多様体のコホモロジー消滅定理

  越川皓永

  金沢整数論オータムワークショップ2021 兼 北陸数論セミナー, 21 Oct. 2021, Invited

  
• Vanishing theorems for unitary Shimura varieties

  Teruhisa Koshikawa

  KAIST Number Theory seminar, 06 Oct. 2021, Invited

  
• Logarithmic prismatic site

  Arithmetic Geometry - Takeshi 60, 09 Sep. 2021, Invited

  
• Logarithmic prismatic cohomology

  越川 皓永

  Arithmetic Geometry and Representation Theory, 16 Dec. 2019, Invited

  
• Recent developments in integral p-adic Hodge theory

  Teruhisa Koshikawa

  代数的整数論とその周辺2019, 12 Dec. 2019, Invited

  
• Remarks on the cohomology of compact unitary Shimura varieties

  Teruhisa Koshikawa

  Artihmetic geometry in Carthage, 28 Jun. 2019, Invited

  
• CM liftings of K3 surfaces and the Tate conjecture

  Teruhisa Koshikawa

  Vietnam-USA Joint Mathematical Meeting, 13 Jun. 2019, Invited

  
• CM liftings of K3 surfaces and the Tate conjecture

  Teruhisa Koshikawa

  Hakodate workshop on arithmetic geometry 2018, 11 Dec. 2018, Invited

  
• Ainf-cohomology in the semistable case

  Teruhisa Koshikawa

  p-adic cohomology and arithmetic geometry, 05 Nov. 2018, Invited

  
• 整p進Hodge理論とK3曲面

  越川 皓永

  東京電機大学・数学講演会, 12 Oct. 2018, Invited

  
• CM liftings of K3 surfaces and the Tate conjecture

  Teruhisa Koshikawa

  Arithmetic Geometry : l-adic and p-adic aspects, 11 Sep. 2018, Invited

  
• 半安定還元の場合の Ainf コホモロジー

  越川 皓永

  代数学シンポジウム, 04 Sep. 2018, Invited

  
• The Ainf-cohomology in the semistable case

  Teruhisa Koshikawa

  The 7th East Asia Number Theory Conference, 06 Feb. 2018, Invited

  
• 半安定還元の場合の Ainf コホモロジー

  越川 皓永

  京都大学数論合同セミナー, 26 Jan. 2018

  
• 整p進Hodge理論について

  越川 皓永

  愛媛大学代数セミナー, 24 Nov. 2017, Invited

  
• Integral p-adic Hodge theory

  Teruhisa Koshikawa

  Topological Hochschild homology and integral p-adic Hodge theory, 23 Sep. 2017, Invited

  
• パーフェクトイド代数とalmost ring theory

  越川 皓永

  可換環論と数論幾何の新展開～ホモロジカル予想を通じて～, 26 Jun. 2017, Invited

  
• Hypersurfaces and the weight-monodromy conjecture

  Teruhisa Koshikawa

  Workshop on Shimura varieties, representation theory and related topics, 23 Nov. 2016, Invited

  
• Heights of Motives

  Teruhisa Koshikawa

  Pan Asia Number Theory Conference, 13 Jul. 2016, Invited

  
• モチーフの高さについて

  越川 皓永

  大阪大学整数論&保型形式セミナー, 08 Jul. 2016, Invited

  
• モチーフと高さ

  越川 皓永

  京都大学談話会, 06 Jul. 2016

  
• 有限体上の多様体の p 進エタール局所系について

  越川 皓永

  京都大学数論合同セミナー, 10 Jun. 2016

  
• Hodge bundles and heights of motives

  Teruhisa Koshikawa

  University of Michigan Algebraic Geometry Seminar, 23 Mar. 2016, Invited

  
• Heights of motives

  Teruhisa Koshikawa

  Stanford University Number Theory Seminar, 21 Sep. 2015, Invited

  
• モチーフの高さについて

  越川 皓永

  第 14 回広島仙台整数論集会, 15 Jul. 2015

  
• Heights of pure motives

  Teruhisa Koshikawa

  The Andre-Oort conjecture, 23 Mar. 2022, Invited

  

Education

Teaching subject(s)

• From 01 Apr. 2024, To 31 Mar. 2025

  Linear Algebra with Exercises A

  N151, Spring, Institute for Liberal Arts and Sciences, 3
• From 01 Apr. 2023, To 31 Mar. 2024

  Linear Algebra with Exercises B

  N152, Fall, Institute for Liberal Arts and Sciences, 3
• From 01 Apr. 2022, To 31 Mar. 2023

  Invitation to Modern Mathematics and Mathematical Sciences

  N114, Spring, Institute for Liberal Arts and Sciences, 2

Academic, Social Contribution

Social Contribution

• 数学オリンピック夏季セミナー講義

  Lecturer

  数学オリンピック財団, From 25 Aug. 2022

  
• 第42回数学入門公開講座

  Lecturer

  京都大学数理解析研究所, From 02 Aug. 2021, To 06 Aug. 2021