O pätnástom Hilbertovom probléme
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Jan Čižmár (1974)
Pokroky matematiky, fyziky a astronomie
Qëndrim R. Gashi (2010)
Annales scientifiques de l'École Normale Supérieure
We prove a conjecture of Kottwitz and Rapoport which implies a converse to Mazur’s Inequality for all (connected) split and quasi-split unramified reductive groups. Our results are related to the non-emptiness of certain affine Deligne-Lusztig varieties.
Alexei N. Skorobogatov (1993)
Annales de la Faculté des sciences de Toulouse : Mathématiques
Gutschwager, Christian (2008)
The Electronic Journal of Combinatorics [electronic only]
Enrique Arrondo, Ignacio Sols (1992)
Mémoires de la Société Mathématique de France
H.C. Hansen (1973)
Mathematica Scandinavica
Pete L. Clark (2006)
Journal de Théorie des Nombres de Bordeaux
Motivated by recent work of Florian Pop, we study the connections between three notions of equivalence of function fields: isomorphism, elementary equivalence, and the condition that each of a pair of fields can be embedded in the other, which we call isogeny. Some of our results are purely geometric: we give an isogeny classification of Severi-Brauer varieties and quadric surfaces. These results are applied to deduce new instances of “elementary equivalence implies isomorphism”: for all genus zero...
Oliver Küchle (1995)
Mathematische Zeitschrift
R. Fioresi, C. Hacon (2004)
Rendiconti del Seminario Matematico della Università di Padova
Krattenthaler, C. (2000)
Séminaire Lotharingien de Combinatoire [electronic only]
Sergey Oblezin (2012)
Open Mathematics
We propose a Givental-type stationary phase integral representation for the restricted Grm,N-Whittaker function, which is expected to describe the (S 1×U N)-equivariant Gromov-Witten invariants of the Grassmann variety Grm,N. Our key tool is a generalization of the Whittaker model for principal series U(gl N)-modules, and its realization in the space of functions of totally positive unipotent matrices. In particular, our construction involves a representation theoretic derivation of the Batyrev-Ciocan-Fontanine-Kim-van...
Crooks, Peter, Milson, Robert (2009)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
Marko Radovanović (2020)
Czechoslovak Mathematical Journal
We prove that for any positive integers there exists a real flag manifold with cup-length equal to its dimension. Additionally, we give a necessary condition that an arbitrary real flag manifold needs to satisfy in order to have cup-length equal to its dimension.
Kevin M. Ryan (1986)
Mathematische Annalen
Mark Gross, Enrique Arrondo (1993)
Manuscripta mathematica
Vinay V. Deodhar (1985)
Inventiones mathematicae
Mikhail V. Ignatyev, Aleksandr A. Shevchenko (2020)
Communications in Mathematics
We consider tangent cones to Schubert subvarieties of the flag variety , where is a Borel subgroup of a reductive complex algebraic group of type , or . We prove that if and form a good pair of involutions in the Weyl group of then the tangent cones and to the corresponding Schubert subvarieties of do not coincide as subschemes of the tangent space to at the neutral point.
Vishik, A. (2005)
Documenta Mathematica
G. M. Henkin, Yu. I. Manin (1981)
Compositio Mathematica
Brian Smyth, Andrew J. Sommese (1984)
Commentarii mathematici Helvetici
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