Zobrazeno 1 - 10
of 33
pro vyhledávání: '"Commelin, Johan"'
Autor:
Commelin, Johan, Topaz, Adam
In this article we discuss how abstraction boundaries can help tame complexity in mathematical research, with the help of an interactive theorem prover. While many of the ideas we present here have been used implicitly by mathematicians for some time
Externí odkaz:
http://arxiv.org/abs/2309.14870
Autor:
Barton, Reid, Commelin, Johan
We introduce a model category of spaces based on the definable sets of an o-minimal expansion of a real closed field. As a model category, it resembles the category of topological spaces, but its underlying category is a coherent topos. We will show
Externí odkaz:
http://arxiv.org/abs/2108.11952
Autor:
Commelin, Johan1 (AUTHOR), Topaz, Adam2 (AUTHOR)
Publikováno v:
Bulletin (New Series) of the American Mathematical Society. Apr2024, Vol. 61 Issue 2, p241-255. 15p.
Autor:
Commelin, Johan, Lewis, Robert Y.
Publikováno v:
Proceedings of Certified Programs and Proofs (CPP 2021)
The ring of Witt vectors $\mathbb{W} R$ over a base ring $R$ is an important tool in algebraic number theory and lies at the foundations of modern $p$-adic Hodge theory. $\mathbb{W} R$ has the interesting property that it constructs a ring of charact
Externí odkaz:
http://arxiv.org/abs/2010.02595
Autor:
Commelin, Johan, Huber, Annette
This paper is a sequel to "Exponential periods and o-minimality I" that the authors wrote together with Philipp Habegger. We complete the comparison between different definitions of exponential periods, and show that they all lead to the same notion.
Externí odkaz:
http://arxiv.org/abs/2007.08290
Let $\alpha \in \mathbb{C}$ be an exponential period. We show that the real and imaginary part of $\alpha$ are up to signs volumes of sets definable in the o-minimal structure generated by $\mathbb{Q}$, the real exponential function and ${\sin}|_{[0,
Externí odkaz:
http://arxiv.org/abs/2007.08280
Publikováno v:
CPP 2020: Proceedings of the 9th ACM SIGPLAN International Conference on Certified Programs and Proofs, Pages 299-312
Perfectoid spaces are sophisticated objects in arithmetic geometry introduced by Peter Scholze in 2012. We formalised enough definitions and theorems in topology, algebra and geometry to define perfectoid spaces in the Lean theorem prover. This exper
Externí odkaz:
http://arxiv.org/abs/1910.12320
The algebraic Sato-Tate conjecture was initially introduced by Serre and then discussed by Banaszak and Kedlaya. This note shows that the Mumford-Tate conjecture for an abelian variety A implies the algebraic Sato-Tate conjecture for A. The relevance
Externí odkaz:
http://arxiv.org/abs/1905.04086
Autor:
Commelin, Johan, Penegini, Matteo
In this paper we study the cohomology of smooth projective complex surfaces $S$ of general type with invariants $p_g = q = 2$ and surjective Albanese morphism. We show that on a Hodge-theoretic level, the cohomology is described by the cohomology of
Externí odkaz:
http://arxiv.org/abs/1901.00193
Autor:
Commelin, Johan
Let $X$ be a smooth projective variety over a finitely generated field $K$ of characteristic~$0$ and fix an embedding $K \subset \mathbb{C}$. The Mumford--Tate conjecture is a precise way of saying that certain extra structure on the $\ell$-adic \'et
Externí odkaz:
http://arxiv.org/abs/1804.06840