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Algebra, Universal --- Lattice theory --- Varieties (Universal algebra)

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Categories (Mathematics) --- Equations, Theory of --- Lattice theory --- Varieties (Universal algebra)

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In this volume, the authors construct a theory of weights on the log crystalline cohomologies of families of open smooth varieties in characteristic p>0, by defining and constructing four filtered complexes. Fundamental properties of these filtered complexes are proved, in particular the p-adic purity, the functionality of three filtered complexes, the weight-filtered base change formula, the weight-filtered Künneth formula, the weight-filtered Poincaré duality, and the E2-degeneration of p-adic weight spectral sequences. In addition, the authors state some theorems on the weight filtration and the slope filtration on the rigid cohomology of a separated scheme of finite type over a perfect field of characteristic p>0.

Filters (Mathematics) --- Varieties (Universal algebra) --- Algebras, Varieties of --- Classes, Equational --- Equational classes --- Varieties of algebras --- Variety (Universal algebra) --- Algebra, Universal --- Mathematics --- Geometry, algebraic. --- Algebra. --- Algebraic Geometry. --- Commutative Rings and Algebras. --- Mathematical analysis --- Algebraic geometry --- Geometry --- Algebraic geometry. --- Commutative algebra. --- Commutative rings. --- Rings (Algebra) --- Algebra

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512.74 --- Moduli theory --- Geometry, Algebraic --- Varieties (Universal algebra) --- Algebras, Varieties of --- Classes, Equational --- Equational classes --- Varieties of algebras --- Variety (Universal algebra) --- Algebra, Universal --- Algebraic geometry --- Geometry --- Theory of moduli --- Analytic spaces --- Functions of several complex variables --- Algebraic groups. Abelian varieties --- 512.74 Algebraic groups. Abelian varieties --- Géométrie algébrique

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This book discusses the ways in which the algebras in a locally finite quasivariety determine its lattice of subquasivarieties. The book starts with a clear and comprehensive presentation of the basic structure theory of quasivariety lattices, and then develops new methods and algorithms for their analysis. Particular attention is paid to the role of quasicritical algebras. The methods are illustrated by applying them to quasivarieties of abelian groups, modular lattices, unary algebras and pure relational structures. An appendix gives an overview of the theory of quasivarieties. Extensive references to the literature are provided throughout.

Quasivarieties (Universal algebra) --- Algebraic systems, Quasi-varieties of --- Classes, Implicationally defined --- Classes, Quasi-primitive --- Classes, Universal Horn --- Horn classes, Universal --- Implicationally defined classes --- Quasi-primitive classes --- Quasi-varieties of algebraic systems --- Quasiprimitive classes --- Universal Horn classes --- Varieties (Universal algebra) --- Logic, Symbolic and mathematical --- Algorithms. --- Algebra. --- Mathematics --- Mathematical analysis --- Algorism --- Algebra --- Arithmetic --- Foundations