Arithmetic Nullstellensätze and Applications
summary
Gives explicit arithmetic Nullstellensatz bounds: for at most n+1 polynomials with degrees dj and heights hj over Z or K(t) produces α∈A\{0} and Gi∈A[X] with degree bound ≲ ∏_j dj and height bounds roughly the product of degrees times the relevant hj (plus an O(n log n) correction over Z), matching the Brownawell-type example where height ≥ d^{n−1}·H. Proof mixes Cramer determinants, Jelonek’s geometric approach and Rabinowitsch/resultant tricks; applications translate finite-field problems (witness theorems, product-set growth in Fp) to characteristic zero and back.
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