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Encyclopedia
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Cohen-macaulay Ring: Encyclopedia Ii - Cohen-macaulay Ring - Formal Definition
A local Cohen-Macaulay ring is defined as a commutative noetherian local ring with Krull dimension equal to its depth. The depth is alway...
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Jean-pierre Serre: 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 variable...
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Encyclopedia
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Jean-pierre Serre: 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 variable...
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Encyclopedia
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Riemann–roch Theorem: Encyclopedia Ii - Riemann–roch Theorem - Statement Of The Theorem
In now-accepted notation, the statement of Riemann–Roch for curves is
l(D) − l(K − D) = deg(D) − g + 1.
This applies to all div...
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Jean-pierre Serre: Encyclopedia Ii - Jean-pierre Serre - Other Work
From 1959 onwards his interests turned towards number theory, in particular class field theory and the theory of complex multiplication.
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Jean-pierre Serre: 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 foundati...
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Jean-pierre Serre: 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 foundati...
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Encyclopedia
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Jean-pierre Serre: Encyclopedia Ii - Jean-pierre Serre - Other Work
From 1959 onwards his interests turned towards number theory, in particular class field theory and the theory of complex multiplication.
...
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Encyclopedia
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Riemann–roch Theorem: 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...
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