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

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

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

.... We prove that under some reasonable assumptions that half of the $$\lambda $$ λ -part of the Bloch–Kato conjecture for the near central critical value...

Galois representations | Primary 11F33 | Congruences among automorphic forms | Saito–Kurokawa correspondence | 11F80 | Mathematics, general | Mathematics | Siegel modular forms | Special values of $$L$$ L -functions | Secondary 11F46 | Bloch–Kato conjecture | 11F67 | Saito-Kurokawa correspondence | Special values of L-functions | Bloch-Kato conjecture | ZETA-FUNCTIONS | EISENSTEIN SERIES | REPRESENTATIONS | GSP | SPECIAL VALUES | MATHEMATICS | CONSTRUCTION | LIFTS | MOTIVES | Valuation

Galois representations | Primary 11F33 | Congruences among automorphic forms | Saito–Kurokawa correspondence | 11F80 | Mathematics, general | Mathematics | Siegel modular forms | Special values of $$L$$ L -functions | Secondary 11F46 | Bloch–Kato conjecture | 11F67 | Saito-Kurokawa correspondence | Special values of L-functions | Bloch-Kato conjecture | ZETA-FUNCTIONS | EISENSTEIN SERIES | REPRESENTATIONS | GSP | SPECIAL VALUES | MATHEMATICS | CONSTRUCTION | LIFTS | MOTIVES | Valuation

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

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

In this paper, we prove the weak p‐part of the Tamagawa number conjecture in all non...

Tamagawa number conjecture | Hecke characters | 14G10 | 11R42 | MSC 11G40 (11R23 | regulators | Iwasawa theory of imaginary quadratic fields | 11G55 | 19F27 | Regulators | CM ELLIPTIC-CURVES | IMAGINARY QUADRATIC FIELDS | MATHEMATICS | HIGHER REGULATORS | BLOCH-KATO CONJECTURE | ADIC K-THEORY | VALUES | MOTIVES | L-SERIES

Tamagawa number conjecture | Hecke characters | 14G10 | 11R42 | MSC 11G40 (11R23 | regulators | Iwasawa theory of imaginary quadratic fields | 11G55 | 19F27 | Regulators | CM ELLIPTIC-CURVES | IMAGINARY QUADRATIC FIELDS | MATHEMATICS | HIGHER REGULATORS | BLOCH-KATO CONJECTURE | ADIC K-THEORY | VALUES | MOTIVES | L-SERIES

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

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

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

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

2015, Volume no. 418

Conference Proceeding

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

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

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

Moscow Mathematical Journal, ISSN 1609-3321, 2011, Volume 11, Issue 2, pp. 317 - 402

The goal of this paper is to give an explicit description of the triangulated categories of Tate and Artin-Tate motives with finite coefficients Z/m over a...

Motives with finite coefficients | Artin-tate motives | Koszul algebras | Nonflat koszul rings | Tate motives | Silly filtrations | Milnor-bloch-kato conjecture | Beilinson-lichtenbaum conjecture | K(π1) conjecture | Koszulity conjecture | Beilinson-Lichtenbaum conjecture | MATHEMATICS, APPLIED | silly filtrations | motives with finite coefficients | K(pi, 1) conjecture | Milnor-Bloch-Kato conjecture | Artin-Tate motives | MATHEMATICS | CATEGORY | KOSZUL DUALITY | K-THEORY | BLOCH-KATO CONJECTURE | nonflat Koszul rings

Motives with finite coefficients | Artin-tate motives | Koszul algebras | Nonflat koszul rings | Tate motives | Silly filtrations | Milnor-bloch-kato conjecture | Beilinson-lichtenbaum conjecture | K(π1) conjecture | Koszulity conjecture | Beilinson-Lichtenbaum conjecture | MATHEMATICS, APPLIED | silly filtrations | motives with finite coefficients | K(pi, 1) conjecture | Milnor-Bloch-Kato conjecture | Artin-Tate motives | MATHEMATICS | CATEGORY | KOSZUL DUALITY | K-THEORY | BLOCH-KATO CONJECTURE | nonflat Koszul rings

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

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

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

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

16.
Full Text
Deformations of polarized automorphic galois representations and adjoint selmer groups

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

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

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

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

11F46 | Mathematics, general | 11F27 | Mathematics | THETA-SERIES | FORMS | MATHEMATICS | REPRESENTATIONS | QUATERNION ALGEBRAS | BLOCH-KATO CONJECTURE | VALUES

Journal Article

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

FORMS | MATHEMATICS | MATHEMATICS, APPLIED | elliptic curve | COHOMOLOGY | Selmer group | REPRESENTATIONS | Bloch-Kato conjecture | CYCLES | CHARACTERS

Journal Article

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