منابع مشابه
Alexander Grothendieck: Enthusiasm and Creativity
Alexander Grothendieck was born in Berlin on 28 March 1928. His father, Sascha Shapiro, an anarchist originally from Russia, took an active part in the revolutionary movements first in Russia, and then in Germany, during the 1920s, where he met Hanka Grothendieck, Alexander’s mother. After the Nazis came to power in Germany it was too dangerous for a Jewish revolutionary to stay there, and the ...
متن کاملGROTHENDIECK POLYNOMIALS AND QUIVER FORMULAS By ANDERS S. BUCH, ANDREW KRESCH, HARRY TAMVAKIS, and ALEXANDER YONG
Fulton’s universal Schubert polynomials give cohomology formulas for a class of degeneracy loci, which generalize Schubert varieties. The K-theoretic quiver formula of Buch expresses the structure sheaves of these loci as integral linear combinations of products of stable Grothendieck polynomials. We prove an explicit combinatorial formula for the coefficients, which shows that they have altern...
متن کاملGrothendieck quasitoposes
Article history: Received 28 June 2011 Available online 31 January 2012 Communicated by Michel Van den Bergh
متن کاملCombinatorial Formulae for Grothendieck-demazure and Grothendieck Polynomials
∂if = f− sif xi − xi+1 where si acts on f by transposing xi and xi+1 and let π̃i = ∂i(xi(1− xi+1)f) Then the Grothendieck-Demazure polynomial κα, which is attributed to A. Lascoux and M. P. Schützenberger, is defined as κα = x α1 1 x α2 2 x α3 3 ... if α1 ≥ α2 ≥ α3 ≥ ..., i.e. α is non-increasing, and κα = π̃iκαsi if αi < αi+1, where si acts on α by transposing the indices. Example 2.1. Let α = (...
متن کاملThe Grothendieck Group
In the red corner, topological K-theory! The study of stable equivalences of vector bundles over a topological space, and the engine behind Bott periodicity, a result whose reverberations are felt throughout algebraic topology. In the blue corner, modular representation theory! The story of representations in positive characteristic, where the CDE triangle powers applications in group theory an...
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ژورنال
عنوان ژورنال: Nature
سال: 2015
ISSN: 0028-0836,1476-4687
DOI: 10.1038/517272a