In algebraic geometry and synthetic differential geometry, a Grothendieck connection is a way of viewing connections in terms of descent data from infinitesimal neighbourhoods of the diagonal.
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Grothendieckconnection is a way of viewing connections in terms of descent data from infinitesimal neighbourhoods of the diagonal. The Grothendieck connection...
Alexander Grothendieck (/ˈɡroʊtəndiːk/; German pronunciation: [ˌalɛˈksandɐ ˈɡʁoːtn̩ˌdiːk] ; French: [ɡʁɔtɛndik]; 28 March 1928 – 13 November 2014) was...
In category theory, a branch of mathematics, a Grothendieck topology is a structure on a category C that makes the objects of C act like the open sets...
algebraic schemes are locally prime spectra of commutative unital rings (A. Grothendieck), and every quasi-separated scheme X {\displaystyle X} can be reconstructed...
and applied to what is now called a Grothendieck topos. The theory was rounded out by establishing that a Grothendieck topos was a category of sheaves, where...
cohomology groups of harmonic forms 1968 Alexander GrothendieckGrothendieckconnection 1968 Alexander Grothendieck Formulates the standard conjectures on algebraic...
replaced by a Zariski topology in the sense of Grothendieck topology. Grothendieck introduced Grothendieck topologies having in mind more exotic but geometrically...
to establish the Dolbeault isomorphism we need to prove the Dolbeault–Grothendieck lemma (or ∂ ¯ {\displaystyle {\bar {\partial }}} -Poincaré lemma). First...
between algebraic geometry and number theory that propelled Alexander Grothendieck to recast the foundations making use of sheaf theory (together with Jean-Pierre...
proved by Bernard Dwork (1960), the functional equation by Alexander Grothendieck (1965), and the analogue of the Riemann hypothesis by Pierre Deligne (1974)...
the set theoretic sense is then replaced by a Grothendieck topology. Grothendieck introduced Grothendieck topologies having in mind more exotic but geometrically...
well understood. Galois theory has been generalized to Galois connections and Grothendieck's Galois theory. The birth and development of Galois theory was...
younger newcomers including Jean-Pierre Serre and Alexander Grothendieck. Serre, Grothendieck and Laurent Schwartz were awarded the Fields Medal during...
by Jean Leray. It is usually seen nowadays as a special case of the Grothendieck spectral sequence. Let f : X → Y {\displaystyle f:X\to Y} be a continuous...
authors have called metric circles Riemannian circles, especially in connection with the filling area conjecture in Riemannian geometry, but this term...
Hans Freudenthal Peter Freyd Pierre Gabriel Israel Gelfand Alexander Grothendieck Allen Hatcher Friedrich Hirzebruch Heinz Hopf Michael J. Hopkins Witold...
Another place in which Tannakian categories have been used is in connection with the Grothendieck–Katz p-curvature conjecture; in other words, in bounding monodromy...
known as the Chern–Weil theory. There is also an approach of Alexander Grothendieck showing that axiomatically one need only define the line bundle case...
Fields Medal, at 27. He retains this distinction. In 1966, Alexander Grothendieck boycotted the ICM, held in Moscow, to protest Soviet military actions...
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