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Journal of the Mathematical Society of Japan, ISSN 0025-5645, 2015, Volume 67, Issue 2, pp. 797 - 860
Let K = Q(i root D-K) be an imaginary quadratic field of discriminant -D-K. We introduce a notion of an adelic Maass space S-k,(M)(-k/2) for automorphic forms... 
Automorphic forms on unitary groups | Maass lift | Congruences | Bloch-Kato conjecture | the Maass lift | MATHEMATICS | YOSHIDA LIFTS | SERIES | REPRESENTATIONS | EXTENSIONS | CONSTRUCTION | automorphic forms on unitary groups | congruences
Journal Article
Compositio mathematica, ISSN 0010-437X, 07/2019, Volume 155, Issue 7, pp. 1327 - 1401
...–Kato conjecture for some Galois characters of $E$ , extending the results of Bellaiche and Chenevier to the case of a positive sign. 
p-adic automorphic forms | Bloch Kato conjecture | UNITARY GROUPS | MAIN CONJECTURES | SHIMURA VARIETIES | FILTRATION | eigenvarieties | Picard modular varieties | MATHEMATICS | COHOMOLOGY | p-divisible groups | CONSTRUCTION | AUTOMORPHIC-FORMS | GALOIS REPRESENTATIONS | Analytic functions | Sheaves
Journal Article
Mathematische Zeitschrift, ISSN 0025-5874, 4/2014, Volume 276, Issue 3, pp. 889 - 924
Journal Article
Journal of Number Theory, ISSN 0022-314X, 08/2013, Volume 133, Issue 8, pp. 2496 - 2537
...}). We provide evidence for the Bloch–Kato conjecture for the motive M=ρf1⊗ρf2(−k/2−1) by proving that under some assumptions the ℓ... 
Special L-values | Galois representations | Siegel modular forms | Bloch–Kato conjecture | Congruences among automorphic forms | Bloch-Kato conjecture | MATHEMATICS | REPRESENTATIONS | SIEGEL MODULAR-FORMS | CONSTRUCTION | Valuation
Journal Article
Mathematische Nachrichten, ISSN 0025-584X, 04/2011, Volume 284, Issue 5‐6, pp. 608 - 628
Journal Article
Selecta Mathematica, ISSN 1022-1824, 7/2016, Volume 22, Issue 3, pp. 1073 - 1115
We present a general conjecture on congruences between Hecke eigenvalues of parabolically induced and cuspidal automorphic representations of split reductive groups, modulo divisors of critical values... 
11F46 | Congruences of modular forms | Mathematics, general | Harder’s conjecture | Mathematics | Bloch–Kato conjecture | 11F75 | 11F67 | 11F33 | MATHEMATICS, APPLIED | LOCAL SYSTEMS | REPRESENTATIONS | Bloch-Kato conjecture | SIEGEL MODULAR-FORMS | L-VALUES | CONJECTURE | MATHEMATICS | ABELIAN SURFACES | SQUARE L-FUNCTIONS | COHOMOLOGY | SHAFAREVICH-TATE GROUPS | DEGREE-2 | Harder's conjecture
Journal Article
Compositio mathematica, ISSN 0010-437X, 3/2007, Volume 143, Issue 2, pp. 290 - 322
...–Kato conjecture for modular forms. We demonstrate an implication that under suitable hypotheses if $\varpi \mid L_{\rm alg}(k,f)$ then $p \mid \# H_{f}(\mathbb{Q},W_{f}(1-k))$ where $p... 
Saito-Kurokawa lifts | Selmer groups | Modular forms | Bloch-Kato conjecture | modular forms | ZETA-FUNCTIONS | EISENSTEIN SERIES | REPRESENTATIONS | SIEGEL CUSP FORMS | MODULAR-FORMS | MATHEMATICS | FOURIER COEFFICIENTS | HALF-INTEGRAL WEIGHT | DEGREE-2 | SYMPLECTIC GROUPS | DIRICHLET SERIES | Hypotheses | Mathematics
Journal Article
Annales scientifiques de l'Ecole normale superieure, ISSN 0012-9593, 2004, Volume 37, Issue 5, pp. 663 - 727
.... We then use the method of Taylor and Wiles to verify the λ-part of the Tamagawa number conjecture of Bloch and Kato for L ( A , 0 ) and L ( A , 1 ) . Here λ... 
MATHEMATICS | ELLIPTIC-CURVES | HECKE L-FUNCTIONS | AUTOMORPHIC REPRESENTATIONS | P-ADIC REPRESENTATIONS | SWINNERTON-DYER | SPECIAL VALUES | BLOCH-KATO CONJECTURE | IWASAWA THEORY | L-SERIES | SYMMETRICAL SQUARE
Journal Article
International Journal of Number Theory, ISSN 1793-0421, 06/2018, Volume 14, Issue 5, pp. 1329 - 1345
.... Under an assumption similar to Vandiver’s conjecture this also provides evidence for the Fontaine–Mazur conjecture for residually reducible polarized Galois representations. 
Galois representations | Bloch-Kato conjecture | Fontaine-Mazur conjecture | FORMS | MATHEMATICS | AUTOMORPHY | COHOMOLOGY | UNITARY GROUPS | ADJOINT MOTIVES
Journal Article
Journal of Number Theory, ISSN 0022-314X, 2011, Volume 131, Issue 7, pp. 1296 - 1330
We explain how the Bloch–Kato conjecture leads us to the following conclusion: a large prime dividing a critical value of the L-function of a classical Hecke... 
Harderʼs conjecture | Saito–Kurokawa lift | Bloch–Kato conjecture | Standard L-function | Saito-Kurokawa lift | Standard l-function | Harder's conjecture | Bloch-Kato conjecture | ZETA-FUNCTIONS | LOCAL SYSTEMS | EISENSTEIN SERIES | REPRESENTATIONS | CONJECTURE | FORMS | MATHEMATICS | ABELIAN SURFACES | COHOMOLOGY | CONSTRUCTION | HALF-INTEGRAL WEIGHT | Universities and colleges
Journal Article
Canadian journal of mathematics, ISSN 0008-414X, 04/2006, Volume 58, Issue 2, pp. 419 - 448
We introduce a new conjecture concerning the construction of elements in the annihilator ideal associated to a Galois action on the higher-dimensional algebraic $K... 
MATHEMATICS | BASE CHANGE | FITTING IDEALS | TOTALLY-REAL FIELDS | EXTENSIONS | INTEGERS | ALGEBRAIC K-THEORY | BRUMER-STARK | BLOCH-KATO CONJECTURE | MOTIVES | NUMBER-FIELDS
Journal Article
Journal of Algebraic Geometry, ISSN 1056-3911, 2016, Volume 25, Issue 3, pp. 571 - 605
We study local-global questions for Galois cohomology over the function field of a curve defined over a p-adic field (a field of cohomological dimension 3). We... 
MATHEMATICS | BLOCH-KATO CONJECTURE | HASSE PRINCIPLE | COHOMOLOGY | KERNEL | DUALITY THEOREMS
Journal Article
Annales de l'Institut Fourier, ISSN 0373-0956, 2017, Volume 67, Issue 3, pp. 1231 - 1276
In this article, we construct an Euler system using CM cycles on Kuga-Sato varieties over Shimura curves and show a relation with the central values of... 
Selmer groups | Bloch-Kato conjecture | Modular forms | ELLIPTIC-CURVES | FIELDS | HEEGNER CYCLES | REPRESENTATIONS | HODGE THEORY | VARIETIES | P-ADIC REGULATORS | MOD L | CONJECTURE | MATHEMATICS | COHOMOLOGY
Journal Article
Duke Mathematical Journal, ISSN 0012-7094, 09/2016, Volume 165, Issue 13, pp. 2407 - 2460
We prove the vanishing of the geometric Bloch-Kato Selmer group for the adjoint representation of a Galois representation associated to regular algebraic... 
FORMS | MATHEMATICS | CONJECTURE | Mathematics - Number Theory
Journal Article
Advances in Mathematics, ISSN 0001-8708, 05/2018, Volume 330, pp. 420 - 432
A smooth projective scheme X over a field k is said to satisfy the Rost nilpotence principle if any endomorphism of X in the category of Chow motives that... 
Motivic cohomology | Rost nilpotence | Algebraic cycles | MATHEMATICS | CHOW GROUPS | COEFFICIENTS | K-THEORY | BLOCH-KATO CONJECTURE | RATIONAL SURFACES
Journal Article
Advances in Mathematics, ISSN 0001-8708, 01/2020, Volume 359, p. 106880
.... For the field of algebraic numbers we formulate a period conjecture for motivic cohomology by saying that this period regulator is surjective... 
Motives | Periods | Motivic and de Rham cohomology | Motivic and dc Rham cohomology | ALGEBRAIC CYCLES | CHARACTERISTIC ZERO | THEOREM | FIELD | TORSION | MATHEMATICS | COHOMOLOGY | REALIZATIONS | K-THEORY | BLOCH-KATO CONJECTURE | HOPF | Algebraic Geometry | Mathematics
Journal Article
Mathematische Zeitschrift, ISSN 0025-5874, 4/2017, Volume 285, Issue 3, pp. 851 - 878
We give an explicit construction of vector-valued Yoshida lifts and derive a formula of the Bessel periods of Yoshida lifts, by which we prove the... 
11F46 | Mathematics, general | 11F27 | Mathematics | THETA-SERIES | FORMS | MATHEMATICS | REPRESENTATIONS | QUATERNION ALGEBRAS | BLOCH-KATO CONJECTURE | VALUES
Journal Article
by Liu, YF
JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY, ISSN 1435-9855, 2019, Volume 21, Issue 5, pp. 1411 - 1508
Let E be a modular elliptic curve over a totally real cubic field. We have a cubic-triple product motive over Q constructed from E through multiplicative... 
FORMS | MATHEMATICS | MATHEMATICS, APPLIED | elliptic curve | COHOMOLOGY | Selmer group | REPRESENTATIONS | Bloch-Kato conjecture | CYCLES | CHARACTERS
Journal Article
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