منابع مشابه
Reduction Mod P of Standard Bases
We investigate the behavior of standard bases (in the sense of Hironaka and Grauert) for ideals in rings of formal power series over commutative rings with respect to specializations of the coefficients. For instance, we show that any ideal I of the ring of formal power series A[[X]] = A[[X1, . . . , XN ]] with coefficients in a Noetherian ring A admits a standard basis whose image under every ...
متن کاملHilbert-kunz Multiplicity and Reduction Mod P
In this paper, we study the behaviour of Hilbert-Kunz multiplicities (abbreviated henceforth to HK multiplicities) of the reductions to positive characteristics of an irreducible projective curve in characteristic 0. For instance, consider the following question. Let f be a nonzero irreducible homogeneous element in the polynomial ring Z[X1, X2, . . . , Xr], and for any prime number p ∈ Z, let ...
متن کاملRANK p − 1 MOD - p H - SPACES
Different constructions by Cooke, Harper and Zabrodsky and by Cohen and Neisendorfer produce torsion free finite p-local H-spaces of rank l < p−1. The first construction goes through when l = p− 1 and we show the second does as well. However, the space produced need not be an H-space. We give a criterion for when an H-space is obtained. In the special case of rank 2 mod-3 H-spaces, we also give...
متن کاملLower Bounds for (MOD p - MOD m) Circuits
Modular gates are known to be immune for the random restriction techniques of Ajtai Ajt83], Furst, Saxe, Sipser FSS84], Yao Yao85] and H astad H as86]. We demonstrate here a random clustering technique which overcomes this diiculty and is capable to prove generalizations of several known modular circuit lower bounds of Barrington, Straubing, Th erien BST90], Krause and Pudll ak KP94], and other...
متن کاملA Degree-Decreasing Lemma for (MOD q - MOD p) Circuits
Consider a (MODq;MODp) circuit, where the inputs of the bottom MODp gates are degree-d polynomials with integer coefficients of the input variables (p, q are different primes). Using our main tool — the Degree Decreasing Lemma — we show that this circuit can be converted to a (MODq;MODp) circuit with linear polynomials on the input-level with the price of increasing the size of the circuit. Thi...
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ژورنال
عنوان ژورنال: Communications in Algebra
سال: 2005
ISSN: 0092-7872,1532-4125
DOI: 10.1081/agb-200061031