Robert Garbary, Department of Pure Mathematics, University of Waterloo
Let A be a commutative algebraic group defined over a number field K. For a prime ℘ in K where A has good reduction, let N℘,n be the number of n-torsion F℘-rational points of the reduction of A modulo ℘ where F℘ is the residue field of ℘ and n is a positive integer. When A is of dimension one and n is relative prime to a fixed finite set of primes depending on A/K, we determine the average values of N℘,n as the prime ℘ varies.
Abstract:
We will see why the title of the talk is true. More specifically, if Q is definable set in a Zariski structure then RM(Q) ≤ dimQ.
Abstract:
Abstract:
Let A be a commutative algebraic group dened over a number eld K. For a prime } in K where A has good reduction, let N};n be the number of n-torsion F}-rational points of the reduction of A modulo } where F} is the residue eld of } and n is a positive integer. When A is of dimension one
We will introduce three axioms on a Noetherian topological structure which, together with the Krull dimension, are sufficient to make the topological structure a one-dimensional presmooth Zariski structure. We will show that such a structure has quantifier elimination, and satisfies the addition formula AF if the fibre condition FC holds.
This is the first lecture in an ongoing learning seminar devoted to learning some recent algorithms for "fixed finite template" constraint satisfaction problems. In this lecture I will give a quick introduction to these problems, and then describe an algorithm for problems whose constraints are cosets of subgroups of powers of a fixed group Wednesday.
Please note room.
We will show that hyperimmune degrees are able to omit non-principal partial types, and in fact are the only such types. By seeing that this proof can be carried out in RCA0, we will show that omitting partial types and the existence of hyperimmune degrees are equivalent over RCA0.