Concept

Arithmetic geometry

Related lectures (32)

Explores elementary algebra concepts related to numeric sets and prime numbers, including unique factorization and properties.

Prime Numbers: Deterministic Approaches

Introduces deterministic approaches to identify prime numbers and covers algorithms and modular arithmetic for prime number testing.

Weil Conjectures: Rationality and Function Equation

Covers the Weil conjectures on rationality, functional equation, and the Riemann hypothesis, exploring properties of varieties in algebraic geometry.

Variety Defined as the Closure of VCA

Explores the concept of variety defined as the closure of VCA and its applications in algebraic geometry.

Modern Algebraic Geometry

Covers modern algebraic geometry, including algebraic sets, morphisms, and projective algebraic sets.

Tangent Spaces in Algebraic Geometry

Explores tangent spaces in algebraic geometry, defining them as finite-dimensional subspaces of derivations on varieties.

Varieties with nef anti-canonical: Surjective Albanese

Presents a proof that smooth projective varieties with nef anti-canonical divisor have surjective Albanese morphism.

Regularity and Geometric Meaning

Explores regularity in algebraic geometry and the geometric implications of the Jacobian criterion.

P-adic integration: Rationality and Igusa zeta function

Explores p-adic integration, Igusa zeta function rationality, and monodromy conjectures.

Quotients of Groups by Relations of Equivalence

Explores quotients of groups by equivalence relations and the conditions for well-defined sets.

Prime Numbers and Algorithms

Covers prime numbers, primality testing algorithms, modular arithmetic, and efficient exponentiation methods.

Number Theory: Prime Numbers and Modular Arithmetic

Explores prime numbers, modular arithmetic, Wilson's theorem, and complexity analysis.

Modern Algebraic Geometry: Schemes and Affine Schemes

Covers modern algebraic geometry, focusing on schemes and affine schemes, including a review of classical algebraic geometry and Bézout's theorem.

Redly Constructed Morphisms

Explores the construction and properties of morphisms, focusing on effective divisors, isomorphism of semi-groups, and the relationship between sheaves and factorial spaces.

Hensel's Lemma Application

Discusses the application of Hensel's lemma in determining nth roots and elements that are nth powers.

Modular Arithmetic: Operations and Properties

Explains modular arithmetic operations and properties, including commutative rings and multiplicative inverses.

Modular Arithmetic: Properties and Examples

Covers modular arithmetic properties, computation examples, and commutative rings.

Algebra: Fundamental Theorem

Covers a general introduction and discusses algebra, emphasizing the importance of unique factorization in algebraic structures.

Geometric Objects in Algebra

Covers the study of graded modules and quasicoherent sheaves in algebraic geometry.

Tangent Spaces Insights

Explores the relationships between tangent spaces, dimensions, and sub-varieties in algebraic geometry.