Home Page for Haruzo HIDA

Forthcoming Workshop: RTG/FRG Workshop organized by D. Blasius, H. Hida and C. Khare at UCLA from June 14th to 20th, 2010:

Modular/geometric Iwasawa theory and p-adic L-functions

COURSES

• Math 207a Fall 2009
• Math 205c Spring 2009
• Math 290b Seminar, Spring 2009
• Math 207c Spring 2007
• Math 132 Winter 2009
• Math 61 Winter 2009

Ph.D. Students

• Koji Kitagawa, 1991 (1963-2007)
• Brad Wilson, 1993
• Chandrashekhar Khare, 1995 Khare's homepage
• Eknath Ghate, 1996 Ghate's homepage
• Sheena Cho, 1999, the thesis of Sheena Cho is a part of her joint work with V. Vatsal. Here is Vatsal's web site which contains the preprint: [Vatsal's home page]
• Ami Fischman, 2001, his paper (which is a part of his thesis) [Fischman's home page]
• Hsin-Tai Wu, 2001,
• Cristian Virdol, 2005, his papers (including his thesis) [Virdol's homepage]
• Hae-Sang Sun, 2007, his papers (including his thesis) [Sun's home page]
• Craig Citro, 2009, his papers [Citro's home page]
• Lin Chen, 2009, his papers [Chen's home page]

H. Hida, Modular Forms and Galois Cohomology, Cambridge Studies in advanced mathematics 69, 2000 (book),
[ Cambridge University Press web site on this book ], A list of misprints (as of March 30, 2009): [pdf]

H. Hida, Geometric Modular Forms and Elliptic Curves, World Scientific Publishing Co., Singapore, 2000 (book),
[ World Scientific web site on this book], A list of misprints (as of February 25, 2005): [dvi]

H. Hida, Adjoint Selmer groups as Iwasawa modules, Israel J. Math. 120 (2000), 361-427 [dvi.gz]

H. Hida, Control theorems for coherent sheaves on Shimura varieties of PEL-type, Journal of the Inst. of Math. Jussieu 1 (2002), 1-76 [dvi.gz]

H. Hida, Non-vanishing modulo p of Hecke L-values, In "Geometric Aspects of Dwork Theory" (A. Adolphson, F. Baldassarri, P. Berthelot, N. Katz and F. Loeser, eds.), pp.735-784, Walter de Gruyter, Berlin, 2004 (preprint:[dvi], publisher site [de Gruyter])

H. Hida, p-Adic Automorphic Forms on Shimura Varieties, Springer Monographs in Mathematics, 2004 (book),
[ Springer web site on this book], A list of misprints (as of 6/26/07): [pdf]

H. Hida, Greenberg's L-invariants of adjoint square Galois representations, IMRN, Issue 59 (2004) 3177--3189, [dvi] (Euclid site; pdf file)

H. Hida, p-Adic automorphic forms on reductive groups, (lecture notes at Poincare Institute, Paris, 3/29/00-6/14/00), Asterisque 298 (2005), 147--254, SMF, Preprint-version [dvi.gz].

H. Hida, The integral basis problem of Eichler, IMRN (2005) No.34 2101-2122, [dvi]:the version of 10/10/04

H. Hida, Non-vanishing modulo p of Hecke L-values and application, London Mathematical Society Lecture Note Series 320 (2007) 207-269, (preprint-version: [dvi]: version of 7/16/04, LMS book site: [LNS 320])

H. Hida, CM periods, L-values and the CM main conjecture, in Hakuba Symposium Proceedings (2006) 13-28, preprint-version: [pdf]

H. Hida, Automorphism Groups of Shimura Varieties of PEL type, Documenta Math. 11 (2006) 25-56 (preprint version: [dvi.zip])

H. Hida, Hilbert Modular Forms and Iwasawa Theory, Oxford Mathematical Monographs, Oxford University Press, 2006
[ Oxford web site on this book] whose US site: [ Oxford web US-site on this book]. A list of misprints (as of 8/15/07): [pdf]

H. Hida, Anticyclotomic Main Conjectures, in the Coates anniversary volume from Documenta Math. Ducumenta Math. Volume Coates (2006), 465-532 (Reprint from Documenta Math:[pdf], preprint version: [dvi] a summary lecture at Banff in 2003 [dvi])

H. Hida, L-invariant of p-adic L-functions, in "THE CONFERENCE ON L-FUNCTIONS" pp.17--53, 2007 (the notes of Lectures at Kyushu university and Harvard university, 2/06-5/06; [World Scientific web page on this book]), a preprint-version: [pdf],

H. Hida, L-invariants of Tate curves, Pure and Applied Math Quarterly 5 (2009) No.4, 1343-1384 (reprint from PAMQ [pdf] and a preprint version of 9/30/07 [pdf])

H. Hida, L-invariant of symmetric powers of Tate curves, Publication of RIMS 45 (2009) No.1, 1-24 (a link to RIMS web site containing the reprint pdf file [pdf], a preprint version of 9/26/07 [pdf])

H. Hida, On a generalization of the conjecture of Mazur-Tate-Teitelbaum, International Mathematics Research Notices (2007) Vol. 2007 : article ID rnm102, 49 pages, doi:10.1093/imrn/rnm102 published on October 30, 2007 (reprint from Oxford site [pdf], abstract [htm], a preprint version of 7/3/2007 [pdf], a summary [pdf]: lecture notes at Iwasawa 2008 conference at Kloster-Irsee, Germany)

H. Hida, Serre's conjecture and base change for GL(2), Pure and Applied Math Quarterly, 5 No.1 (2009), 81-125 the published version [pdf] (a preprint version of 3/15/08: [pdf]), a talk on a similar topic at a conference in Northwestern university with some result obtained after the paper was written (a version of 5/14/2008 [pdf])

H. Hida, The Iwasawa mu-invariant of p-adic Hecke L-functions, to appear in Annals of Mathematics (version of 10/17/2008 minor typo corrected) [pdf], a link to the Annals webpage containing the pdf file [Annals]; two lecture notes at Paris-Nord/Kyoto university, one 2-hour and another 1.5 hour on the vanishing [pdf])

H. Hida, Irreducibility of the Igusa tower, Acta Mathematica Sinica, English Series, 25 (2009), 1--20 (pdf reprint:[pdf], a preprint version of 5/25/08 [pdf]) and the summary of the paper and Section 8.4 of my Springer book [pdf] (a talk at a Luminy conference on 7/18/06 with title "Irreducibility of the Siegel-Igusa tower"; a more detailed version of 11/5/07)

H. Hida, L-invariant of tensor power of Hilbert modular forms, (preprint version of 8/14/08:[pdf]), Hokkaido University Technical Report Series in Mathematics 137 (2008), 150-172

H.Hida, Irreducibility of the Igusa tower over unitary Shimura varieties, a research article version of the lectures at UCLA on unitary Igusa tower (a version of 1/20/08: [pdf]), to appear in the Shahidi anniversary volume from Clay Institute (the three UCLA lecture notes: [pdf],[pdf],[pdf], the lectures given in October-November 2007)

H. Hida, Quadratic exercises in Iwasawa theory, International Mathematics Research Notices (2009), doi:10.1093/imrn/rnn151 (reprint from Oxford site [pdf], [htm], abstract [htm], a preprint version of 11/9/08 [pdf], Inchon lecture note [pdf])

Click to download:

H. Hida, Modular Galois representations of "Neben" type, (a summary of Sections 5.1.1 and 5.2.1-2 from my book on geometric modular forms) [dvi] [pdf]

H. Hida, Control Theorems and Applications, Lectures at Tata institute of fundamental research (Version of 2/15/00) [dvi.gz]

H. Hida, Modularity problems of Q-motives and base-change, (four lectures at Strasbourg, France, 1/31-2/4/00) [dvi]

H. Hida, Reciprocity laws and prime decomposition, (Notes of a perspective colloquium talk at UCLA, 2/26/01) [dvi] [pdf]

H. Hida, A simple proof of non-vanishing modulo p of Dirichlet L-functions, Number Theory seminar talk at UC Irvine 5/8/03; [dvi]

H. Hida, CM periods and the anticyclotomic main conjecture, (Conference talk at Luminy, France, 6/18/02) talk manuscript:[dvi], abstract:[dvi]

H. Hida, L-invariants and p-ordinary families of Hilbert modular forms, (Conference talk at Banff, Canada, 12/15/03) [dvi]

H. Hida, Modular Iwasawa theory, (a series of lectures at Peking University, Beijing, China, 2/15-20/04) [dvi]

H. Hida, L-invariants of adjoint square Galois representations, (Talk at AMS regional meeting, special session, USC, 4/3/04) [dvi]

H. Hida, Non-vanishing modulo p of Values of L-functions,, Graduate perspective seminar talk 2/14/05, [dvi]

H. Hida, Extensions and the exceptional zero of the adjoint square L-functions, a conference talk on 7/4/05 at Strasbourg, France, [pdf]

H. Hida, Nonvanishing of L-values mod p, the notes of the two lectures at Tata institute of fundamental research 8/18-21/06 (a revised version of the lecture at the conference: "Automorphic Galois Representations, L-functions and Arithmetic" held at Columbia University; lecture delivered on 6/17-18/2006) [pdf]

H. Hida, Taylor-Wiles patching lemmas a la Kisin, Lecture notes of two talks at Ghate's Number Theory seminar 5/14,16/2007 (version of 5/13/07 [pdf])

H. Hida, Control of nearly ordinary Hecke algebras, Lecture notes of a talk at Luminy Summer school on Serre's conjecture (delivered on 7/17/2007) (version of 7/18/07, minor error corrected [pdf])

H. Hida, Permutation representations and Langlands base change, lecture note of a talk at Northwestern university on 5/11/2008 (a version of 5/14/2008 [pdf])

H. Hida, Five lectures at Tata institute 7/30-8/7/2008, No.1[pdf], No.2[pdf], No.3[pdf], No.4[pdf], No.5 (Colloquium talk) [pdf].

H. Hida, Vanishing of the mu-Invariant of p-Adic Hecke L-functions, preprint, 2009 (version of 5/1/2009 [pdf])

H. Hida, Two lectures on Metaplectic groups and Siegel-Weil formulas, in 2001 at Ritsumeikan university (Japan): [pdf],[pdf] (revised version of 4/30/2007)

H. Hida, Hecke fields of analytic families of modular forms, preprint, 2009 (version of 10/17/2009 [pdf]: some notation clarified in the proof of Lemma 4.1, and also typos corrected, in particular, in the second proof of Lemma 4.1 and in the proof of Theorem 2.3, a summary of the result [BC-MIT talk] on 10/20/09).

H. Hida, Lambda-adic p-divisible groups, I: [pdf], II: [pdf], two lectures at CRM (Montreal) in September 2005

Older Publications

H. Hida, On the values of Hecke's L-functions at non-positive integers, J. Math. Soc. Japan, 30 (1978), 249-278 [JMS site](pdf file)

H. Hida, On abelian varieties with complex multiplication as factors of the abelian variety attached to Hilbert modular forms, Japan. J. Math. (new series) 5 (1979), 157-208 [JMS site] (pdf file; Master thesis)

H. Hida, On abelian varieties with complex multiplication as factors of the jacobians of Shimura curves, Amer. J. Math. 103 (1981), 727-776 (Doctral Thesis) [JSTOR site] (pdf, subscription necessay to download)

H. Hida, Congruences of cusp forms and special values of their zeta functions, Inventiones Math. 63 (1981), 225-261 [GDZ site] (pdf file)

H. Hida, On congruence divisors of cusp forms as factors of the special values of their zeta functions, Inventiones Math. 64 (1981), 221-262 [GDZ site] (pdf file)

H. Hida, Kummer's criterion for the special values of Hecke L-functions of imaginary quadratic fields and congruences among cusp forms, Inventiones Math. 66 (1982), 415-459 [GDZ site] (pdf file)

H. Hida, Transformation equations and the special values of Shimura's zeta functions, joint work with K. Doi and Y. Maeda, Hokkaido Math. J. 13 (1984), 347-361

H. Hida, A p-adic measure attached to the zeta functions associated with two elliptic modular forms I, Inventiones Math. 79 (1985), 159-195 [GDZ site]

H. Hida, Congruences of cusp forms and Hecke algebras, Sem. de Theorie des Nombres, Paris 1983-84, Progress in Math. 59 (1985) 133-146

H. Hida, Convolution de Rankin p-adique, Sem. de Theorie des Nombres de Bordeaux 1984-85 Expose no.13 [GDZ site] (pdf file)

H. Hida, Iwasawa modules attached to congruences of cusp forms, Ann. Scient. Ec. Norm. Sup. 4th series 19 (1986), 231-273 [Numdum site] (pdf file)

H. Hida, Galois representations into GL_2(Z_p[[X]]) attached to ordinary cusp forms, Inventiones Math. 85 (1986), 545-613 [GDZ site] (pdf file)

H. Hida, Hecke algebras for GL_1 and GL_2, Sem. de Theorie des Nombres, Paris 1984-85, Progress in Math. 63 (1986), 131-163

H. Hida, On p-adic Hecke algebras for GL_2, Proc. International Congress of Mathematicians, 1986, 434--443

H. Hida, A p-adic measure attached to the zeta functions associated with two elliptic modular forms II, Ann. l'institut Fourier 38 (1988), 1-83 [Numdam site] (pdf file)

H. Hida, Modules of congruence of Hecke algebras and L-functions associated with cusp forms, Amer. J. Math. 110 (1988), 323--382 [JSTOR] (pdf file, subscription to JSTOR necessary)

H. Hida, On $p$--adic Hecke algebras for $GL_2$ over totally real fields, Ann. of Math. 128 (1988), 295--384 [JSTOR] (pdf file, subscription to JSTOR necessary)

H. Hida, On nearly ordinary Hecke algebras for GL(2) over totally real fields, Advanced Studies in Pure Math. 17 (1989), 139-169 [ASPM site]

H. Hida, Nearly ordinary Hecke algebras and Galois representations of several variables, Proc. JAMI Inaugural Conference, Supplement to Amer. J. Math. (1989), 115-134

H. Hida, Theory of p-adic Hecke algebras and Galois representations, Sugaku Expositions 2 (1989), 75-102

H. Hida, Le produit de Petersson et de Rankin p-adique, Sem. Theorie de Nombre de Paris, 1988-89, 87-102

H. Hida, p-adic L-functions for base change lifts of GL_2 to GL_3, in Proc. of Conference on "Automorphic forms, Shimura varieties, and $L$--functions", Perspectives in Math. 11 (1990), 93-142

H. Hida and J. Tilouine, Katz p-adic L-functions, congruence modules and deformation of Galois representations, Proc. LMS Symposium on ``L-functions and arithmetic'', Durham, England, July 1989, LMS Lecture notes series 153 (1991), 271-293

H. Hida, On p-adic L-functions of GL(2) x GL(2) over totally real fields, Ann. Inst. Fourier 41 (1991), 311-391 [Numdam] (pdf file)

H. Hida and J. Tilouine, Anti-cyclotomic Katz p-adic L-functions and congruence modules, Ann. Scient. Ec. Norm.Sup. 26 (1993), 189--259 [Numdam] (pdf file)

H. Hida, p-Ordinary cohomology groups for SL(2) over number fields, Duke Math. J. 69 (1993), 259-314 [Euclid site] (pdf file)

H. Hida, Elementary Theory of L-functions and Eisenstein series, 1993, Cambridge University Press, Book [Cambridge web page]

H. Hida and J. Tilouine, On the anti-cyclotomic main conjecture for CM fields, Inventiones Math. 117 (1994), 89-147 [GDZ site] (pdf file)

H. Hida, On the critical values of L-functions of GL(2) and GL(2) x GL(2), Duke Math. J. 74 (1994), 431-529 [Euclid site] (pdf file)

H. Hida, p-Adic ordinary Hecke algebras for GL(2), Ann. l'insitut Fourier 44 (1994), 1289-1322 [Numdam] (p df file)

H. Hida, Modular p-adic L-functions and p-adic Hecke algebras, Amer. Math. Soc. Transl. 160 (1994), 125-154

H. Hida, On Lambda-adic forms of half integral weight for SL(2), in Number Theory, Paris, Lecture notes series of LMS 215 (1995), 139-166

H. Hida, Control theorems of p-nearly ordinary cohomology groups for SL(n), in Bull. Soc. Math. Fr. 123 (1995), 425-475 [pdf] reprint from Numdam collection

H. Hida, On Selmer groups of adjoint modular Galois representations, in "Number Theory 1993-94", Paris, Lecture notes series of LMS 235 (1996), 89-132 [pdf]; Correction [pdf]

H. Hida, On the search of genuine p-adic modular L-functions for GL(n), Monograph, Memoires SMF 67 (1996) [dvi.gz] (reprint from Numdam site: [pdf])

H. Hida, J. Tilouine and E. Urban, Adjoint modular Galois representations and their Selmer groups, Proc. Natl. Acad. Sci. USA 94 (1997), 11121-11124 [PNAS site] (pdf file)

H. Hida and Y. Maeda, Non-abelian base change for totally real fields, Olga Taussky Todd memorial issue, Pacific Journal of Math. (1997), 189-217 [dvi.gz]

H. Hida, Global quadratic units and Hecke algebras, Documenta Math. 3 (1998), 273-284 (preprint version: [dvi] [pdf];[Documenta Math. site])

K. Doi, H. Hida and H. Ishii, Discriminant of Hecke fields and the twisted adjoint L-values for GL(2), Inventiones Math. 134 (1998), 547-577 [dvi][pdf]

H. Hida, Automorphic induction and Leopoldt type conjectures for GL(n), Asian J. Math. 2 (1998), 667--710 [ Asian J. site] (pdf file)

H. Hida, Non-critical values of adjoint L-functions for SL(2), Proc. Symp. Pure Math. 66 (1999) Part I, 123-175 [dvi]