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coherent sheaf | A Wisdom Archive on coherent sheaf | | coherent sheaf A selection of articles related to coherent sheaf | |
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| | |  coherent sheaf: Encyclopedia II - Jean-Pierre Serre - Early workFrom a very young age he was an outstanding figure in the school of Henri Cartan, working on algebraic topology, several complex variables and then commutative algebra and algebraic geometry, in the context of sheaf theory and homological algebra techniques. Serre's thesis refers to his dissertation on the Leray-Serre spectral sequence associated to a fibration.
In his speech at the Fields Medal award ceremony in 1954, Hermann Weyl praised Serre in apparently extravagant terms, and also made the point that the award ...
See also:Jean-Pierre Serre, Jean-Pierre Serre - Life and career, Jean-Pierre Serre - Early work, Jean-Pierre Serre - Foundational work in algebraic geometry and the Weil conjectures, Jean-Pierre Serre - Other work, Jean-Pierre Serre - Awards, Jean-Pierre Serre - Works, Jean-Pierre Serre - External link Read more here: » Jean-Pierre Serre: Encyclopedia II - Jean-Pierre Serre - Early work |
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| | | | coherent sheaf: Encyclopedia II - Jean-Pierre Serre - Early work From a very young age he was an outstanding figure in the school of Henri Cartan, working on algebraic topology, several complex variables and then commutative algebra and algebraic geometry, in the context of sheaf theory and homological algebra techniques. Serre's thesis refers to his dissertation on the Leray-Serre spectral sequence associated to a fibration.
In his speech at the Fields Medal award ceremony in 1954, Hermann Weyl praised Serre in apparently extravagant terms, and also made the point that the award ...
See also:Jean-Pierre Serre, Jean-Pierre Serre - Life and career, Jean-Pierre Serre - Early work, Jean-Pierre Serre - Foundational work in algebraic geometry and the Weil conjectures, Jean-Pierre Serre - Other work, Jean-Pierre Serre - Awards, Jean-Pierre Serre - External link Read more here: » Jean-Pierre Serre: Encyclopedia II - Jean-Pierre Serre - Early work |
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| | | | coherent sheaf: Encyclopedia II - Jean-Pierre Serre - Foundational work in algebraic geometry and the Weil conjectures In the 1950s and 1960s, a fruitful collaboration between Serre and the two years younger Alexander Grothendieck led to important foundational work, much of it motivated by the Weil conjectures. Two major foundational papers by Serre were FAC (Faisceaux Algébriques Cohérents, on coherent cohomology) and GAGA.
Serre had early on perceived a need to construct more general and refined cohomology theories to tackle these conjectures. In simple terms, the cohomology of a coherent sheaf over a finite field couldn't capture as much t ...
See also:Jean-Pierre Serre, Jean-Pierre Serre - Life and career, Jean-Pierre Serre - Early work, Jean-Pierre Serre - Foundational work in algebraic geometry and the Weil conjectures, Jean-Pierre Serre - Other work, Jean-Pierre Serre - Awards, Jean-Pierre Serre - Works, Jean-Pierre Serre - External link Read more here: » Jean-Pierre Serre: Encyclopedia II - Jean-Pierre Serre - Foundational work in algebraic geometry and the Weil conjectures |
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| | | | coherent sheaf: Encyclopedia II - Jean-Pierre Serre - Foundational work in algebraic geometry and the Weil conjectures In the 1950s and 1960s, a fruitful collaboration between Serre and the two years younger Alexander Grothendieck led to important foundational work, much of it motivated by the Weil conjectures. Two major foundational papers by Serre were FAC (Faisceaux Algébriques Cohérents, on coherent cohomology) and GAGA.
Serre had early on perceived a need to construct more general and refined cohomology theories to tackle these conjectures. In simple terms, the cohomology of a coherent sheaf over a finite field couldn't capture as much t ...
See also:Jean-Pierre Serre, Jean-Pierre Serre - Life and career, Jean-Pierre Serre - Early work, Jean-Pierre Serre - Foundational work in algebraic geometry and the Weil conjectures, Jean-Pierre Serre - Other work, Jean-Pierre Serre - Awards, Jean-Pierre Serre - External link Read more here: » Jean-Pierre Serre: Encyclopedia II - Jean-Pierre Serre - Foundational work in algebraic geometry and the Weil conjectures |
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| | | | coherent sheaf: Encyclopedia II - Riemann–Roch theorem - Some data We start with a connected compact Riemann surface of genus g, and a fixed point P on it. We may look at functions having a pole only at P. There is an increasing sequence of vector spaces: functions with no poles (i.e., constant functions), functions allowed at most a simple pole at P, functions allowed at most a double pole at P, a triple pole, ... These spaces are all finite dimensional. In case g = 0 we can see that the sequence of dimensions starts
1, 2, 3, ...:
this can be read off from the theory of partial fractions. Conversely i ...
See also:Riemann–Roch theorem, Riemann–Roch theorem - Some data, Riemann–Roch theorem - Statement of the theorem, Riemann–Roch theorem - A long road of generalisation Read more here: » Riemann–Roch theorem: Encyclopedia II - Riemann–Roch theorem - Some data |
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