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4 papers
Higher spectral sequences
Benjamin Matschke
In this article we construct what we call a higher spectral sequence for any chain complex (or topological space) that is filtered in compatible ways. For this we extend the pr…
Elliptic curves with good reduction outside of the first six primes
Alex J. Best, Benjamin Matschke
We present a database of rational elliptic curves, up to Q-isomorphism, with good reduction outside {2,3,5,7,11,13}. We provide a heuristic involving the abc and BSD conjectures th…
Proofs by example
Benjamin Matschke
We study the proof scheme "proof by example" in which a general statement can be proved by verifying it for a single example. This strategy can indeed work if the statement in ques…
Solving S-unit, Mordell, Thue, Thue-Mahler and generalized Ramanujan-Nagell equations via Shimura-Taniyama conjecture
Rafael von Känel, Benjamin Matschke
In the first part we construct algorithms which we apply to solve S-unit, Mordell, cubic Thue, cubic Thue-Mahler and generalized Ramanujan-Nagell equations. As a byproduct we obtai…