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Science China Mathematics, ISSN 1674-7283, 11/2019, Volume 62, Issue 11, pp. 2409 - 2422
This is an expository article on the recent progress on the arithmetic fundamental lemma conjecture, based largely on Zhang (2019... 
relative trace formula | Gross-Zagier formula | Mathematics | arithmetic fundamental lemma | 11G40 | Applications of Mathematics | arithmetic Gan-Gross-Prasad conjecture | 14G35 | 11F67
Journal Article
Algebra and Number Theory, ISSN 1937-0652, 2017, Volume 11, Issue 10, pp. 2425 - 2445
W. Zhang's arithmetic fundamental lemma (AFL) is a conjectural identity between the derivative of an orbital integral on a symmetric space with an arithmetic intersection number on a unitary Rapoport-Zink space... 
Special cycles | Arithmetic fundamental lemmas | Arithmetic Gan–Gross–Prasad conjectures | Rapoport–Zink spaces | MATHEMATICS | Rapoport-Zink spaces | special cycles | arithmetic Gan-Gross-Prasad conjectures | arithmetic fundamental lemmas
Journal Article
02/2019, ISBN 9780691181387, 281
Outer billiards provides a toy model for planetary motion and exhibits intricate and mysterious behavior even for seemingly simple examples. It is a dynamical... 
Mathematics | Combinatorial number theory
eBook
Compositio mathematica, ISSN 0010-437X, 10/2013, Volume 149, Issue 10, pp. 1631 - 1666
The arithmetic fundamental lemma conjecture of the third author connects the derivative of an orbital integral on a symmetric space with an intersection number on a formal moduli space of $p... 
arithmetic fundamental lemma | Rapoport-Zink spaces | special cycles | arithmetic Gan-Gross-Prasad conjecture | MATHEMATICS | Mathematics | Arithmetic
Journal Article
Annali di matematica pura ed applicata, ISSN 1618-1891, 2010, Volume 190, Issue 3, pp. 539 - 551
.... By means of a division lemma for convergent power series, we find the exact relation existing between the zeros of two octonionic regular functions and those of... 
Fundamental theorem of algebra | Functions of a hypercomplex variable | Quaternions | Octonions | Mathematics, general | 30G35 | 32A30 | Mathematics | 30C15 | POLYNOMIALS | MATHEMATICS | MATHEMATICS, APPLIED | FUNDAMENTAL THEOREM | ALGEBRA | SETS
Journal Article
Mathematische Zeitschrift, ISSN 1432-1823, 2007, Volume 258, Issue 2, pp. 395 - 406
We improve Margulis lemma for a compact connected Lie group G: there is a neighborhood U of the identity such that for any finite subgroup $$\Gamma\subset G$$ , $$U\cap \Gamma... 
Mathematics, general | Mathematics | MATHEMATICS | MANIFOLDS | FUNDAMENTAL-GROUPS | SPACES | NONNEGATIVE CURVATURE
Journal Article
Canadian journal of mathematics, ISSN 0008-414X, 08/2018, Volume 70, Issue 4, pp. 898 - 924
In this paper, we prove the spherical fundamental lemma for metaplectic group $M{{p}_{2n}}$ based on the formalism of endoscopy theory by J... 
Elliptic stable trace formula | Endoscopic group | Metaplectic group | Fundamental lemma | metaplectic group | endoscopic group | P-ADIC GROUPS | MATHEMATICS | elliptic stable trace formula | REPRESENTATIONS | THEOREM | REDUCTIVE GROUPS | fundamental lemma | TRACE FORMULA
Journal Article
Neutrosophic sets and systems, ISSN 2331-6055, 12/2019, Volume 30, pp. 44 - 69
... and Burnside’s lemma of NET group. We introduce NET orbits, stabilizers, conjugates and NET group action... 
net group action; net orbit; net stabilizer; net conjugate; burnside’s lemma; net fixed points; the fundamental theorem about net group action
Journal Article
Mathematische Zeitschrift, ISSN 1432-1823, 2017, Volume 287, Issue 1-2, pp. 181 - 197
We prove that the arithmetic fundamental lemma conjecture (AFL) of Wei Zhang is equivalent to a similar conjecture, but for Lie algebras, in the case of non-degenerate intersection... 
14G17 | Intersection product | Unitary Rapoport–Zink space | 11G18 | Mathematics, general | Mathematics | Arithmetic fundamental lemma | 14G40 | Orbital integral | MATHEMATICS | ENDOMORPHISMS | Unitary Rapoport-Zink space | Algebra
Journal Article
Journal of Algebra, ISSN 0021-8693, 05/2014, Volume 406, pp. 251 - 271
Journal Article
Journal für die reine und angewandte Mathematik (Crelles Journal), ISSN 0075-4102, 10/2019, Volume 2019, Issue 755, pp. 1 - 65
To every singular reduced projective curve one can associate, following Esteves, many fine compactified Jacobians, depending on the choice of a polarization on... 
MATHEMATICS | BUNDLES | REPRESENTATIONS | THEOREM | MODULI SPACE | DUALITY | SPECTRAL CURVES | FUNDAMENTAL LEMMA | TRANSFORMS
Journal Article
Transactions of the American Mathematical Society, ISSN 0002-9947, 08/2017, Volume 369, Issue 8, pp. 5341 - 5402
To every singular reduced projective curve X one can associate many fine compactified Jacobians, depending on the choice of a polarization on X, each of which... 
Locally planar singularities | Abel map | Compactified jacobians | MATHEMATICS | SCHEME | AUTODUALITY | BUNDLES | locally planar singularities | Compactified Jacobians | DUALITY | ABEL MAPS | FUNDAMENTAL LEMMA
Journal Article
Algebraic Geometry, ISSN 2313-1691, 01/2018, Volume 5, Issue 1, pp. 77 - 113
.... In particular, we generalize Luna's fundamental lemma when applied to a diagonalizable group: we obtain criteria for a G-equivariant morphism f : X... 
Luna's fundamental lemma | Diagonalizable groups | MATHEMATICS | FACTORIZATION | HOMOMORPHISMS | QUILLEN | diagonalizable groups | BIRATIONAL MAPS | TORIFICATION | HOMOLOGY | SCHEMES
Journal Article
Advances in Differential Equations, ISSN 1079-9389, 11/2018, Volume 23, Issue 11-12, pp. 889 - 908
In the paper, we derive a fractional version of the Du BoisReymond lemma for a generalized Riemann-Liouville derivative... 
EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | ORDER ALPHA | VARIATIONAL CALCULUS | TERMS | FORMULA | EULER-LAGRANGE EQUATIONS | DERIVATIVES | FUNDAMENTAL LEMMA
Journal Article
Transactions of the American Mathematical Society, ISSN 0002-9947, 09/2019, Volume 371, Issue 9, pp. 6169 - 6212
This article gives a proof of the Langlands-Shelstad fundamental lemma for the spherical Hecke algebra for every unramified p-adic reductive group G in large positive characteristic... 
MATHEMATICS | ENDOSCOPY | FUNDAMENTAL LEMMA
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 06/2016, Volume 438, Issue 1, pp. 274 - 284
A triple of commuting operators for which the closed tetrablock E‾ is a spectral set is called a tetrablock contraction or an E-contraction. The set E is... 
Fundamental operators | Operator model | Tetrablock contraction | Canonical decomposition | MATHEMATICS | MATHEMATICS, APPLIED | SCHWARZ-LEMMA
Journal Article
Inventiones mathematicae, ISSN 0020-9910, 6/2013, Volume 192, Issue 3, pp. 627 - 661
.... In combination with a general base-change lemma in harmonic analysis, we use this to prove a conjecture of Haines and Kottwitz for these Shimura varieties. 
Mathematics, general | Mathematics | MATHEMATICS | REPRESENTATIONS | FUNDAMENTAL LEMMA | Fourier analysis
Journal Article
Inventiones Mathematicae, ISSN 0020-9910, 05/2017, Volume 208, Issue 2, pp. 501 - 552
We prove the Noether-Lefschetz conjecture on the moduli space of quasi-polarized K3 surfaces. This is deduced as a particular case of a general theorem that... 
MATHEMATICS | ARITHMETIC QUOTIENTS | K-3 SURFACES | REPRESENTATIONS | PRODUCTS | K3 SURFACES | PICARD-GROUPS | VARIETIES | MODULI SPACE | AUTOMORPHIC-FORMS | FUNDAMENTAL LEMMA | Manifolds | Homology | Arithmetic | Theorems
Journal Article
Mathematics of Computation of the American Mathematical Society, ISSN 0025-5718, 03/2016, Volume 85, Issue 298, pp. 907 - 929
In the 1980s Bocherer formulated a conjecture relating the central values of the imaginary quadratic twists of the spin L-function attached to a Siegel modular... 
MATHEMATICS, APPLIED | NOVODVORSKY SUBGROUPS | FOURIER COEFFICIENTS | SIEGEL MODULAR-FORMS | BESSEL | FUNDAMENTAL LEMMA | CONJECTURE
Journal Article
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