Search results for “algebra”
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97 results
CMI 2000, The Millennium Prize Problems
2026Problem sheet
The Millennium Meeting, Paris, 24 May 2000, at which the seven problems were announced.
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Quotients of admissible formal schemes and adic spaces by finite groups
2024Journal articleBogdan Zavyalov
Algebra & Number Theory
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A curiosity: “supersmooth” varieties
Theory
A rigidity condition on schemes, strictly stronger than smoothness, introduced with examples and a look at where it fails to be geometric — no known application, just a curiosity.
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Finite flat commutative group schemes embed locally into abelian schemes
Theory
A proof of Raynaud's theorem: every finite flat commutative group scheme over a locally noetherian base embeds, Zariski-locally, as a closed subgroup of an abelian scheme.
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An example of a non-reduced Picard scheme
Theory
An example, due to Serre, of a smooth projective surface in positive characteristic whose Picard scheme fails to be reduced, worked out via the two governing dimension inequalities.
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Determinant
Theory
The determinant of a square matrix — its meaning, minors and cofactors, Laplace expansion, and computation methods.
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Determinant via Permutations
Theory
The direct definition of a determinant via permutations: inversions, parity, and a sum of n! terms.
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Systems of Linear Equations
Theory
Linear systems in matrix form, the Kronecker–Capelli theorem, homogeneous systems, and the fundamental system of solutions.
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