Algebraic independence in positive characteristic: A $p$-adic calculus

DOI10.1090/S0002-9947-2014-06268-5zbMath1350.13015arXiv1202.4301MaRDI QIDQ5420121

Peter Scheiblechner, Nitin Saxena, J. Mittmann

Publication date: 11 June 2014

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1202.4301

zbMATH Keywords

Jacobianfinite fieldzeta functionGalois ringcrystalline cohomologyKählerde Rhamalgebraic independence\(p\)-adicdifferentialTeichmülleridentity testingWitt

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Polynomial rings and ideals; rings of integer-valued polynomials (13F20) de Rham cohomology and algebraic geometry (14F40) Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.) (68Q17) (p)-adic cohomology, crystalline cohomology (14F30) Witt vectors and related rings (13F35)

Related Items (6)

The number of parts in certain residue classes of integer partitions ⋮ Algebraic independence over positive characteristic: new criterion and applications to locally low-algebraic-rank circuits ⋮ Rational equivalence for enveloping algebras of three-dimensional Lie algebras ⋮ Jacobian Hits Circuits: Hitting Sets, Lower Bounds for Depth-$D$ Occur-$k$ Formulas and Depth-3 Transcendence Degree-$k$ Circuits ⋮ Unnamed Item ⋮ Monomials in arithmetic circuits: complete problems in the counting hierarchy

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The complexity of computing the permanent
• Extractors and rank extractors for polynomial sources
• On computing the determinant in small parallel time using a small number of processors
• Counting points on \(C_{ab}\) curves using Monsky-Washnitzer cohomology
• Deterministically testing sparse polynomial identities of unbounded degree
• La conjecture de Weil. II
• The complexity of partial derivatives
• A constructive approach to Noether's problem
• La conjecture de Weil. I
• On the intractability of Hilbert's Nullstellensatz and an algebraic version of ``\(NP\neq P\)?
• Extractors for varieties
• Algebraic independence and blackbox identity testing
• A \(p\)-adic proof of Weil's conjectures
• Approximate formulas for some functions of prime numbers
• On the Sum of Square Roots of Polynomials and Related Problems
• On P vs. NP and geometric complexity theory
• Arithmetic Circuits: A survey of recent results and open questions
• Computing zeta functions of nondegenerate curves
• Finding Isomorphisms Between Finite Fields
• Progress on Polynomial Identity Testing - II
• A Lower Bound for the Formula Size of Rational Functions
• Complexe de de\thinspace Rham-Witt et cohomologie cristalline
• Fast Probabilistic Algorithms for Verification of Polynomial Identities
• Computational Complexity
• Jacobian hits circuits
• Relative Rigid Cohomology and Deformation of Hypersurfaces
• On the Rationality of the Zeta Function of an Algebraic Variety

This page was built for publication: Algebraic independence in positive characteristic: A $p$-adic calculus