# 2012$BG/EY@0?tO@%5%^!<%9%/!<%k(B $B!V(BStark$BM=A[!W(B ## $B?7Ce>pJs(B

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• 2012$BG/#57n#1#5F|!';22C?=9~$N
• 2012$BG/#67n#9F|!';22C?=9~$N
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$B!&(B16:30-18:00 $BM-M}?tBN>e$N(BStark$BM=A[$N>ZL@(B($B2C1v(B)
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$B!&(B09:00-10:30 Galois cohomology$B$N=Hw(B($B;3K\(B)
$B!&(B10:45-12:15 $BM-M}?tCM;XI8$N>l9g(B($B;3K\(B)
$B!&8a8e$O<+M3F$O@(B 9/5($B?e(B)
$B!&(B09:30-10:30 Rubin's integral refinement($B2C1v(B)
$B!&(B10:45-12:15 Brumer-Stark$BM=A[#1(B($B;01:(B) $B!&(B13:30-15:00 Brumer-Stark$BM=A[#2(B($B;01:(B)
$B!&(B15:15-16:45 $BHs2D49(BBrumer$BM=A[(B($BLnB<(B)
$B!&(B17:00-18:30 Brumer-Stark$BM=A[$H(BGross$BM=A[$K$D$$F(B(B7*86(B) 9/6(BLZ(B) B!&(B09:00-10:30 WilesBN(Bbig Galois representation(B;3>e(B) B!&(B10:45-12:15 GrossBM=A[(B(Dasgupta-Darmon-PollackBN7k2L(B)(B2OB<(B) B!&Ck?)8e!J(B13:30 B4m!K2r;6(B ### BM=Dj5lF$$$k9V1iNN,!K(B $B7*86>-?M(B($B7DXf5A=NBg3X(B)$B!"(B $B;3>eFX;N(B($B5~ET;:6HBg3X(B)$B!"(B $B>.3^867r(B($B6e=#Bg3X(B)$B!"(B $B>.Ln;{0l9@(B($BEl5~9)6HBg3X(B)$B!"(B $B2OB<>0L@(B($BKL3$F;Bg3X(B)$B!"(B $B:4F#?.IW(B($B5~ETBg3X(B)$B!"(B $BLnB< ### $B>,$N;~4V(B $B%"%J%&%s%9$5$l$F$$k9V1i0J30K!"4uK>R2p!"LdBjDs5/JI2?Gb7k9=G9!#(B B>\:YKD$$$F$O!";22C?=9~;~ ### $B;29MJ88%(B

$B!&@0?tO@A4HL(B $B2CF#(B $BOBLi(B, $B:XF#(B $B5#(B, $B9u@n(B $B?.=E(B, $B?tO@#1(B(Fermat$B$NL4$HN`BNO@(B), $B4dGH(B.
$B9u@n(B $B?.=E(B, $B:XF#(B $B5#(B, $B7*86(B $B>-?M(B, $B?tO@#2(B($B4dBtM}O@$HJ]7?7A<0(B), $B4dGH(B.
$B!!(B $B!&(BStark$BM=A[A4HL(B Stark, H. M., L-functions at s=1, I,II,III,IV, Advances in Math., 7(1971), 301-343, 17(1975), 60-92, 22(1976), 64-84, 35(1980), 197-235. Tate, J., On Stark's conjectures on the behavior of$L(s,\chi)$at$s=0$, J. Fac. Sci. Univ. Tokyo, 28 (1981), 963-978. Rubin, K., A Stark conjecture $B!H(Bover Z$B!I(B for abelian L-functions with multiple zeros, Annales de L'Institut Fourier 46 (1996), 33-62. Dasgupta, S., Stark's Conjectures (thesis). J. Tate, Les conjectures de Stark sur les fonctions L d'Artin en s=0 (Notes by D. Bernardi et N. Schappacher), Progress in Math. 47, Birkh\"auser, 1984. Stark's Conjectures, Recent Work And New Directions, An International Conference On Stark's Conjectures And Related Topics, August 5-9, 2002, Johns Hopkins Univ., Contemporary Mathematics. Popescu, C., Rubin, K., Silverberg, A., Arithmetic of L-Functions, Ias / Park City Mathematics Series vol. 18, AMS, 2011. $B!!(B
$B!&Hs2D49(BStark$BM=A[(B(rank 1)$B$N6qBN7W;;Nc(B
T. Chinberg, Stark's conjecture for L-functions with first-order zeroes at s = 0, Adv. in Math. 48 (1983), no. 1, 82-113.
$B!!(B $B!&e$N>l9g(B Shintani, T., On values at s = 1 of certain L functions of totally real algebraic number fields, Algebraic Number Theory, Proc. International Sympos., Kyoto, 1976, Kinokuniya, Tokyo, 1977, 201-212. Shintani, T, On certain ray class invariants of real quadratic fields., J. Math, Soc. Japan 30 (1978), 139-167. $B?7C+BnO:(B, $BBe?tBN$N(B L $BH!?t$NFC Kubert, D. S., Lang, S., Modular Units, Springer, (1981).
Ren, T., Sczech, R., A refinement of Stark's conjecture over complex cubic number fields, J. Number Theory 129 (2009), no. 4, 831-857.
Hida, H., Elementary theory of L-functions and Eisenstein series, London Mathematical Society Student Texts, 26 (1993).
Yoshida, H., Absolute CM-Periods, Mathematical Surveys and Monographs, vol. 106, 2003, AMS.
$B!!(B $B!&(B(Strong) Brumer-Stark$BM=A[(B Greither, C., Some cases of Brumer's conjecture for abelian CM extensions of totally real fields, Mathematische Zeitschrift, 233, 2000. Greither, C., Computing Fitting ideals of Iwasawa modules, Mathematische Zeitschrift, 246, 2004. Greither, C., Determining Fitting ideals of minus class groups via the equivariant Tamagawa number conjecture, Compositio Math. 143, 2007. Greither, C., Kurihara, M., Stickelberger elements, Fitting ideals of class groups of CM-fields, and dualisation. Math. Z. 260 (2008), no. 4, 905-930. Kurihara, M., On stronger versions of Brumer's conjecture. Tokyo J. Math. 34 (2011), no. 2, 407-428. Kurihara, M., Miura, T., Stickelberger ideals and Fitting ideals of class groups for abelian number fields, Math. Ann. 350 (2011), no. 3, 549-575. Greither, C., Popescu, C., The Galois module structure of l-adic realizations of Picard 1-motives and applications, Intl. Math. Res. Notices, 2011. Greither, C., Popescu, C., An Equivariant Main Conjecture in Iwasawa Theory and Applications, (preprint). $B!!(B
$B!&Hs2D49(BBrumer(-Stark)$BM=A[(B
Nickel, A., On non-abelian Stark-type conjectures, Ann. Inst. Fourier 61 (6), (2011), 2577-2608.
Nickel, A., On the equivariant Tamagawa number conjecture in tame CM-extensions, II,Compos. Math. 147 (4), (2011), 1179-1204.
Nickel, A., Equivariant Iwasawa theory and non-abelian Stark-type conjectures, preprint, 2011.
Burns, D., On derivatives of Artin L-series, Invent. math. 186 (2011) 291-371.
Burns, D., On derivatives of p-adic L-series at s =0, preprint.
$B!!(B $B!&(BGross$BM=A[(B Gross, B. H., p-adic L-series at s = 0. J. Fac. Sci. Univ. Tokyo Sect. IA Math., 28(3):979-994 (1982). Dasgupta, S., Darmon, H., Pollack, R., Hilbert modular forms and the Gross-Stark conjecture Annals of Math. (2) 174 (2011), no. 1, 439-484. $B!!(B
$B!&&+?JJ]7?7A<0$dJ]7?7A<0$KIU?o$9$k%,%m%"I=8=(B Wiles, A., On p-adic representations for totally real fields. Ann. Math. 123, 407-456 (1986). Wiles, A., On ordinary$\lambda$-adic representations associated to modular forms, Invent. Math. 94 (1988), no. 3, 529-573. Hida, H., Elementary Theory of L-functions and Eisenstein Series, LMSST 26, Cambridge University Press, 1993. Hida, H., Modular Forms and Galois Cohomology, Cambridge Studies in advanced mathematics 69, Cambridge University Press, 2000. Hida, H., Hilbert Modular Forms and Iwasawa Theory, Oxford Mathematical Monographs, Oxford University Press, 2006. ## $B%5%^!<%9%/!<%k@$OC?M(B • $B2C1v(B $BJ~OB(B($BEl5~M}2JBg3X(B)
• $B;3K\(B $B=$;J(B($B7DXf5A=NBg3X(B)
• $B@DLZ(B $B9(at ma.noda.tus.ac.jp