My Works




I study ARITHMETIC GEOMETRY.
Especially, I am mainly interested in:

  • $p$-adic Hodge theory and related topics ($(phi,Gamma)$-modules, $p$-adic differential equations...),
  • Iwasawa theory and Bloch-Kato's Tamagawa number conjecture,
  • multiple zeta values, fundamental groups, and mixed Tate motives,
  • Shimura varieties, Drinfel'd modular varieties, moduli of shutkas, and ($p$-adic) Langlands correspondence,
  • modularity lifting theorems (R=T),
  • algebraic cycles, mixed motives, and algebraic $K$-theory,
  • IU Teichmüller theory, and related theories (anabelian geometry, $p$-adic Teichmüller theory...).

    Articles
    A proof of abc conjecture after Mochizuki.
    In preparation.

    On finite multiple zeta values of non-positive weight.
    preprint.

    A simple proof of convolution identities of Bernoulli numbers.
    preprint.

    A small remark on the filtered $\phi$-module of Fermat varieties and Stickelberger's theorem.
    preprint.

    A small remark on finite multiple zeta values and $p$-adic multiple zeta values.
    to appear in RIMS Kôkyûroku Bessatsu.

    Reduction of two dimensional crystalline representations and Hypergeometric polynomials.
    (with Seidai Yasuda) In preparation.

    $p$-adic Hodge theory for open varieties.
    Comptes Rendus Math., volume 349 (2011), issues 21-22, 1127--1130.

    $p$-adic multiple zeta values, $p$-adic multiple $L$-values, and motivic Galois groups.
    "Galois-Teichmüller Theory and Arithmetic Geometry", Adv. Studies in Pure Math. 63 (2012), 629--658.

    $p$-adic Lefschetz (1,1) theorem in semistable case, and Picard number jumping locus.
    Math. Res. Let. 18 (2011), no. 01, 107--124.

    On some applications of integral $p$-adic Hodge theory to Galois representations.
    (with Seidai Yasuda) to appear in J. Number Theory.

    Bounds for the dimensions of the $p$-adic multiple $L$-value spaces.
    Documenta Math. Extra Volume: Andrei A. Suslin's Sixtieth Birthday (2010) 687--723.

    $p$-adic etale cohomology and crystalline cohomology for open varieties with semistable reduction.
    (with Seidai Yasuda) preprint.

    Presentations (reserch talks and survey talks)

    2015

    Inter-universal Teichmuller theory and its Diophantine consequences. (35 hours in total)
    (The 3rd week of the series lectures at Kyushu Univ. is merged into this week at RIMS workshop.)
    (16-20/Mar/2015 at RIMS, verifications and further developments of inter-universal Teichmuller theory)

    Inter-universal Teichmuller theory and its Diophantine consequences. (33.5 hours in total)
    (The 2nd week of the series lectures at Kyushu Univ. is merged into this week at RIMS workshop.)
    (9-13/Mar/2015 at RIMS, verifications and further developments of inter-universal Teichmuller theory)

    2014

    Inter-universal Teichmuller theory and its Diophantine consequences--1st week. (18 hours in total)
    (16-19/Sep/2014 at Kyushu University, series lectures)

    2013

    p-adic multiple zeta values and motivic Galois groups. (60 minutes)
    (25/Jul/2013 at RIMS, Various aspects of multiple zeta values)

    On abc Conjecture. (30 minutes)
    (non-public talk under the security. I refuse all of inqueries on this talk.)
    (6/May/2013 at Toyota Physical and Chemical Research Institute, Colloquium)

    Reductions of two dimensional crystalline representations and Hypergeometric polynomials. (60 minutes)
    (26/Mar/2013 at Keio University, Number Theory Forum)

    $p$-adic multiple zeta values and motivic Galois groups. (60 minutes)
    (11/Feb/2013 at Kushu University, Kyushu Algebraic Number Theory 2013)

    2012

    Etale Cohomology and Weil Conjecture, Part II. (15 hours in total)
    (12-16/Nov/2012 at Keio University)

    Reductions of two dimensional crystalline representations and Hypergeometric polynomials. (60 minutes)
    (12/Sep/2012 at KIAS, Number theory seminar)

    Reductions des representations cristallines en dimension deux et Polynomes Hypergeometriques. (60 minutes)
    (5/Mar/2012 at Institut de Mathematiques de Jussieu, seminaire de theorie des nombres)

    Reduction of two dimensional crystalline representations and Hypergeometric polynomials. (60 minutes)
    (2/Mar/2012 at University of Nottingham, Number theory seminar)

    Reduction of two dimensional crystalline representations and Hypergeometric polynomials. (60 minutes)
    (22/Feb/2012 at Imperial College of London, Number theory seminar)

    Wiles' proof of Fermat's Last Theorem for beginners. (50 minutes)
    (15/Feb/2012 at Kagoshima University, 7th Kagoshima Algebra-Analysis-Geometry Seminar)
    Kagoshima2012small.pdf

    2011

    Etale Cohomology and Weil Conjecture. (15 hours in total)
    (1-5/Nov/2011 at Keio University)

    Crystalline cohomology, Universal extension, and $p$-adic Hodge comparison for the $p$-divisible groups. (8 hours in total)
    (14-15/Jul/2011 at Hokkaido Univerisity, arithmetic geometry seminar)

    $p$-adic multiple zeta values valued in B_{crys}. (90 minutes)
    (23/Jun/2011 at Okayama Univerisity, Algebra seminar)

    Categories for the working arithmetic geometer. (60 minutes)
    (1/Jun/2011 at RIMS, Adventures of Categories -Applied Category Theory Colloquium-)

    Automorphy Lifting and integral $p$-adic Hodge theory. (60 minutes)
    (25/May/2011 at Keio University, Algebra Seminar)

    Automorphy Lifting and integral $p$-adic Hodge theory. (60 minutes)
    (22/Apr/2011 at Kyushu University, Algebra Seminar)

    local-global compatibility after Barnet-Lamb, Gee, Geraghty, and Taylor. (120 minutes)
    (20/Apr/2011 at Kyushu University, arithmetic geometry seminar)

    Le relevement d'automorphie et la theorie de Hodge $p$-adique integrale. (60 minutes)
    (18/Mar/2011 at Universite de Bordeaux, seminaire de theorie des nombres)

    Theorie de Hodge $p$-adique pour les varietes ouvertes. (60 minutes)
    (7/Mar/2011 at Institut de Mathematiques de Jussieu, seminaire de theorie des nombres)

    Le relevement d'automorphie et la theorie de Hodge $p$-adique integrale. (90 minutes)
    (3/Mar/2011 at Institut de Mathematiques de Jussieu, seminaire automorphe)

    Pure Mathematics and Applied Mathematics--from a personal point of view--. (50 minutes)
    (16/Feb/2011 at Kagoshima University, 6-th Kagoshima Algebra-Analysis-Geometry Seminar)

    Gross-Zagier formula. (18 hours in total)
    (4-6/Jan/2011 at Hokkaido University, arithmetic geometry seminar)

    2010

    On the jumping locus of the Picard number. (60 minutes)
    (17/Dec/2010 at University of Tokyo, International workshop on motives in Tokyo, part6)

    $p$-adic Hodge theory for open varieties. (60 minutes)
    (26/Nov/2010 at Osaka University, number theory seminar)

    global-local compatibility after Carayol. (120 minutes)
    (26/Nov/2010 at Osaka University, number theory preseminar)

    $p$-adic multiple zeta values and motivic Galois group. (60 minutes)
    (23/Oct/2010 at International Institute for Advances Studies, Galois-theoric Arithmetic Geometry)

    Introduction to irreducible admissible representations of GL2 of local fields. (250 minutes)
    (3/Aug/2010 at Osaka University, Workshop on arithmetics around GSp(4))

    Introduction to $p$-adic Hodge theory. (90 minutes)
    (13/Jul/2010 at Nagoya University, Arithmetic Geometry seminar)

    Motivic Galois groups and $p$-adic multiple zeta values. (60 minutes)
    (9/Feb/2010 at Durham University, Arithmetic Study Group)

    2009

    Motivic Galois groups and $p$-adic multiple zeta values. (60 minutes)
    (17/Dec/2009 at University of Tokyo, International workshop on motives part 5)

    $p$-adic Hodge theory for open varieties. (60 minutes)
    (13/May/2009 at Cambridge University, algebraic geometry seminar)

    $p$-adic multiple zeta values and motivic Galois groups of mixed Tate motives. (60 minutes)
    (12/May/2009 at Cambridge University, number theory seminar)

    $B_\mathrm{crys}$ lift of $p$-adic Beilinson conjecture. (90 minutes)
    (22/Apr/2009 at University of Nottingham, number theory seminar)

    Integral $p$-adic Hodge theory and automorphy lifting for unitary groups. (90 minutes)
    (14/Jan/2009 at University of Nottingham, number theory seminar)

    2008

    Bounds for the dimensions of the $p$-adic multiple zeta value space. (60 minutes)
    (8/Oct/2008 at Imperial College, number theory seminar)

    Kisin's modified Taylor-Wiles system. (60 minutes)
    (3/Oct/2008 at University of Nottingham, number theory seminar)

    Bounds for the dimensions of the $p$-adic multiple zeta value ($L$-value) space. (90 minutes)
    (4/June/2008 at University of Nottingham, number theory seminar)

    $p$-adic Hodge theory for open varieties. (60 minutes)
    (17/Apr/2008 at University of Nottingham, the Nottingham-Poznan Number theory day)

    Proof of Serre's conjecture of level one case after Khare. (90 minutes)
    (20/Mar/2008 at Yatsugatake, Workshop on Recent Progresions on R=T)

    First step of the induction of the proof of Serre's conjecture after Tate, Serre, and Schoof. (90 minutes)
    (20/Mar/2008 at Yatsugatake, Workshop on Recent Progresions on R=T)

    Taylor-Wiles system for unitary groups after Clozel-Harris-Taylor I. (90 minutes)
    (19/Mar/2008 at Yatsugatake, Workshop on Recent Progresions on R=T)

    Modularity lifting of residually reducible case after Skinner-Wiles. (90 minutes)
    (19/Mar/2008 at Yatsugatake, Workshop on Recent Progresions on R=T)

    Modularity lifting for crystalline deformations of intermediate weights after Kisin. (90 minutes)
    (18/Mar/2008 at Yatsugatake, Workshop on Recent Progresions on R=T)

    Modularity lifting for potentially Barsotti-Tate deformations after Kisin I. (90 minutes)
    (18/Mar/2008 at Yatsugatake, Workshop on Recent Progresions on R=T)
    -> Proceding of "Recent Progressions on R=T --Sato-Tate conjecture and Serre's conjecture--"
    RT2_yamashita.pdf RT22_errata.pdf (in Japanese)

    Galois representations associated to Hilbert modular forms via congruence after Taylor, and Global-local compatibility after Carayol. (90 minutes)
    (17/Mar/2008 at Yatsugatake, Workshop on Recent Progresions on R=T)

    Review of Taylor-Wiles system. (90 minutes)
    (17/Mar/2008 at Yatsugatake, Workshop on Recent Progresions on R=T)
    -> Proceding of "Recent Progressions on R=T --Sato-Tate conjecture and Serre's conjecture--"
    RT1_yamashita.pdf RT22_errata.pdf (in Japanese)

    2007

    $p$-adic multiple zeta value and motivic Galois group. (60 minutes)
    (30/Aug/2007 at Queen's University, Departmental Seminar)

    Bounds for the dimensions of the $p$-adic multiple zeta value ($L$-value) spaces. (60 minutes)
    (25/Jul/2007 at RIMS, Colloquium)

    An introduction to Kimura-O'Sullivan's finite dimensionality of pure motives-2. (60 minutes)
    (6/Jul/2007 at University of Tokyo, Workshop on Motives III)

    An introduction to Kimura-O'Sullivan's finite dimensionality of pure motives-1. (60 minutes)
    (3/Jul/2007 at University of Tokyo, Workshop on Motives III)

    An introduction to $p$-adic Hodge theory. (8 hours in total)
    (14-15/Jun/2007 at Hokkaido University, arithmetic geometry seminar)

    Bounds for the dimensions of the $p$-adic multiple zeta value ($L$-value) spaces. (60 minutes)
    (4/Jun/2007 at Tambara, p-adic aspects in arithmetic geometry)

    Bounds for the dimensions of the $p$-adic multiple zeta value ($L$-value) spaces. (60 minutes)
    (5/Mar/2007 at Hiroshima University, Motives, related topics, applications)

    $p$-adic Hodge theory/$p$-adic multiple zeta values. (Poster)
    (14/Feb/2007 at Seoul National University, the 4-th RIMS-SNU Joint Symposium)

    2006

    $p$-adic Hodge theory for open varieties. (60 minutes)
    (21/Nov/2006 at RIMS, $p$-adic Arithmetic Geometry)

    $p$-adic Hodge theory for open varieties. (60 minutes)
    (11/Oct/2006 at RIMS, Colloquium)

    Reduced Power Operations 2. (60 minutes)
    (28/Sep/2006 at University of Tokyo, Workshop on Motives II)

    Reduced Power Operations 1. (60 minutes)
    (27/Sep/2006 at University of Tokyo, Workshop on Motives II)

    Review and Overview. (60 minutes)
    (25/Sep/2006 at University of Tokyo, Workshop on Motives II)

    $p$-adic Hodge theory for open varieties. (60 minutes)
    (6/Aug/2006 at University of Tokyo, 51-th Algebra Symposium)
    ->Proceeding of "51-th Algebra Symposium", p.111-p.131
    algsymp2006.dvi algsymp2006.pdf algsymp2006.ps (in Japanese)

    Bounds for the dimensions of the $p$-adic multiple zeta value ($L$-value) spaces. (55 minutes)
    (4/Jul/2006 at Limoges, le congres Iwasawa 2006)

    Bounds for the dimensions of the $p$-adic multiple zeta value (and multiple $L$-value) spaces. (60 minutes)
    (26/Apr/2006 at IHES, seminaire de mathematique)

    $p$-adic Hodge theory for open varieties (without Faltings' almost etale theory). (60 minutes)
    (7/Apr/2006 at Universite Paris 13, seminaire de geometrie arithmetique)

    Upper bounds for dimensions of the space of $p$-adic multiple zeta values (and multiple $L$-values). (60 minutes)
    (27/Mar/2006 at Institut de Mathematiques de Jussieu, seminaire de theorie des nombres)

    $p$-adic Hodge theory for open varieties (without Faltings' almost etale theory). (60 minutes)
    (1/Feb/2006 at IHES, seminaire de mathematique)

    2005

    the category of mixed Tate motives over the ring of integers. (60 minutes)
    (21/Dec/2005 at University of Tokyo, Workshop on Motives I)

    Introduction to Voevodsky's category of mixed motives 1. (60 minutes)
    (19/Dec/2005 at University of Tokyo, Workshop on Motives I)

    Bounds for the dimensions of the $p$-adic multiple $L$-value spaces. (60 minutes)
    (25/Nov/2005 at University of Tokyo, Tokyo Seoul Conference Arithmetic and Algebraic Geometry)

    Bounds for the dimensions of the $p$-adic multiple $L$-value spaces. (30 minutes)
    (23/Aug/2005 at Hakui, Number Theory Summer Seminar 2005)
    hamahatasan.dvi hamahatasan.pdf hamahatasan.ps

    Bounds for the dimensions of the $p$-adic multiple $L$-value spaces. (60 minutes)
    (18/May/2005 at Okayama University, Okayama Workshop on Arithmetic and Geometry

    2004

    Bounds for the dimensions of the $p$-adic multiple $L$-value spaces. (50 minutes)
    (6/Dec/2004 at RIMS, Algebraic Number Theory and Related Topics)
    -> RIMS kokyu-roku (2005) No.1451, p.37-41.
    morishitasan.dvi morishitasan.pdf morishitasan.ps

    $p$-adic multiple zeta values, $p$-adic multiple $L$-values, and dimension conjectures. (120 minutes)
    (11/Nov/2004 at RIMS, Study of Multiple Zeta Values)
    -> RIMS kokyu-roku (2007) No.1549, p.153-168.
    ohnosan.dvi ohnosan.pdf ohnosan.ps (in Japanese)

    Bounds for the dimensions of the $p$-adic multiple $L$-value spaces. (60 minutes)
    (23/Jul/2004 at Hiroshima University, 3-rd Number Theory Symposium)

    $p$-adic Hodge theory for open varieties. (60 minutes)
    (6/Mar/2004 at Okayama University, 9-th Conference for Young Researchers)
    okayama.dvi okayama.ps okayama.pdf (in Japanese)

    2003

    $p$-adic Hodge theory for open varieties. (15 minutes)
    (18/Aug/2003 at Sendai, Number Theory Summer Seminar 2003)
    yoinojikan.dvi yoinojikan.ps yoinojikan.pdf (in Japanese)

    $p$-adic etale cohomology and crystalline cohomology for open varieties. (60 minutes)
    (9/Apr/2003 at Nagoya University, $p$-adic Methods in Number Theory)

    $p$-adic etale cohomology and crystalline cohomology for open varieties. (45 minutes)
    (14/Mar/2003 at Waseda University, Algebraic Number Theory Symposium)
    ->Proceeding of "Waseda Algebraic Number Theory Symposium"
    waseda.dvi wadeda.ps waseda.pdf

    2002

    $p$-adic etale cohomology and crystalline cohomology for open varieties. (60 minutes)
    (5/Dec/2002 at RIMS, Algebraic Number Theory and Related Topics)
    -> RIMS kyokyu-roku (2003) No.1324 p.130-141.
    kyoto.dvi kyoto.ps kyoto.pdf

    $p$-adic etale cohomology and crystalline cohomology for open varieties. (60 minutes)
    (8/Oct/2002 at Hokkaido University, Hodge Theory and Algebraic Geometry)
    hokudai.dvi hokudai.ps hokudai.pdf

    2001

    Introduction to $(\phi,\Gamma)$-modules. (60 minutes)
    (6/Dec/2001 at Nagoya University, $p$-adic Representations and $p$-adic Differential Equations)
    phigamma.dvi phigamma.ps phigamma.pdf (in Japanese)


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