by Jacob Lurie, Akhil Mathew
Publisher: Harvard University 2010
Number of pages: 172
Topics: Unique factorization; Basic definitions; Rings of holomorphic functions; R-modules; Ideals; Localization; SpecR and the Zariski topology; The ideal class group; Dedekind domains; Hom and the tensor product; Exactness; Projective modules; Right-exactness of the tensor product; Flatness; Discrete valuation rings; The adjoint property; etc.
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This course is an overview of Homological Conjectures, in particular, the Zero Divisor Conjecture, the Rigidity Conjecture, the Intersection Conjectures, Bass' Conjecture, the Superheight Conjecture, the Direct Summand Conjecture, etc.
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Frobenius splitting has inspired a vast arsenal of techniques in commutative algebra, algebraic geometry, and representation theory. The purpose of these lectures is to give a gentle introduction to Frobenius splitting for beginners.
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