Related papers: A simplified proof of Serre's Conjectures
The aim of this short paper is to give a practical introduction to functional interpretation of proofs for computer scientists interested in synthesis.
We present an improved incremental selection algorithm of the selection algorithm presented in [1] and prove all the selected conjectures.
The purpose of this note is to give the full and self-contained proof of Shchepin's result on a spectral representation of retracts of cubes.
We present a proof of Moessner's theorem by double induction, using only basic rules of arithmetic. No prerequisite knowledge is assumed. Familiarity with summation is advised.
Computing modular coincidences can show whether a given substitution system, which is supported on a point lattice in R^d, consists of model sets or not. We prove the computatibility of this problem and determine an upper bound for the…
We prove a stronger version of a termination theorem appeared in the paper "On existence of log minimal models II". We essentially just get rid of the redundant assumptions so the proof is almost the same as in there. However, we give a…
These notes present some elements of causality theory. While they are not as complete as other treatments of the topic, there is some originality in that the whole approach is based on a definition of causal curves which allows to simplify…
Let $\rho$ be a mod $\ell$ Galois representation attached to a newform $f$. Explicit methods are sometimes able to determine the image of $\rho$, or even the number field cut out by $\rho$, provided that $\ell$ and the level $N$ of $f$ are…
The aim of this note is to give a quick algebraic proof of (the combinatorial part of) the classification theorem for compact real surfaces, whose classical proofs (as in the Massey book and in the Conway ZIP proof) are based on surgery…
We introduce a general formalism with minimal requirements under which we are able to prove the pro-modular Fontaine-Mazur conjecture. We verify it in the ordinary case using the recent construction of Breuil and Herzig.
The main purpose of this note is to pose a couple of problems which are easily formulated thought some seem to be not yet solved. These problems are of general interest for discrete mathematics including a new twig of a bough of theory of…
In this short note we reduce the b-semiampleness conjecture for lc-trivial fibrations to the b-semiampleness conjecture for klt-trivial fibrations.
The goal of this expository article is to present a proof that is as direct and elementary as possible of the fundamental theorem of complex multiplication (Shimura, Taniyama, Langlands, Tate, Deligne et al.). The article is a revision of…
The recently developed proof of Fermat's Last Theorem is very lengthy and difficult, so much so as to be beyond all but a small body of specialists. While certainly of value in the developments that resulted, that proof could not be, nor…
The aim of this short note is to provide a proof to a statement of Sierpi\'nski concerning the number of possible sums of a series (of type $\lambda<\aleph_1$) of arbitrary ordinal numbers.
We prove a modularity lifting theorem for potentially Barostti-Tate representations over totally real fields, generalising recent results of Kisin. Unfortunately, there was an error in the original version of this paper, meaning that we can…
In this paper, we give a short proof of a relation generalizing many identities for Bernoulli numbers.
The aim of this short note is to establish a 2-equivalence between a certain 2-category of foams and that of singular Soergel bimodules of type A.
A new simple proof of Stirling's formula via the partial fraction expansion for the tangent function is presented.
We present a new modular proof method of termination for second-order computation, and report its implementation SOL. The proof method is useful for proving termination of higher-order foundational calculi. To establish the method, we use a…