AN ALGEBRAIC-METRIC EQUIVALENCE RELATION OVER p-ADIC FIELDS

Factoring Polynominals over p-Adic Fields

We give an efficient algorithm for factoring polynomials over finite algebraic extensions of the p-adic numbers. This algorithm uses ideas of Chistov’s random polynomial-time algorithm, and is suitable for practical implementation.

Simultaneous diagonal equations over p-adic fields

with coefficients aij in O. Write the degree as k = pm with p m. A solution x = (x1, . . . , xN) ∈ K is called non-trivial if at least one xj is non-zero. It is a special case of a conjecture of Emil Artin that (∗) has a non-trivial solution whenever N > Rk. This conjecture has been verified by Davenport and Lewis for a single diagonal equation over Qp and for a pair of equations of odd degree ...

Nearly Quadratic Mappings over p-Adic Fields

and Applied Analysis 3 As a special case, if n 2 in 1.3 , then we have the functional equation 1.2 . Also, if n 3 in 1.3 , we obtain 2 ∑ i1 2 3 ∑ i2 i1 1 f ⎛ ⎝ 3 ∑ i 1, i / i1,i2 xi − 2 ∑ r 1 xir ⎞ ⎠ 3 ∑ i1 2 f ⎛ ⎝ 3 ∑ i 1, i / i1 xi − xi1 ⎞ ⎠ f ( 3 ∑

Comparison of some quotients of fundamental groups of algebraic curves over p-adic fields

FINITENESS THEOREM ON ZERO-CYCLES OVER p-ADIC FIELDS

Contents Introduction 2 1. Homology theory and cycle map 6 2. Kato homology 11 3. Vanishing theorem 15 4. Bertini theorem over a discrete valuation ring 19 5. Surjectivity of cycle map 22 6. Blowup formula 24 7. A moving lemma 26 8. Proof of main theorem 28 9. Applications of main theorem 31 Appendix A. Resolution of singularities for embedded curves 34 References 39