[HTML][HTML] Abelian surfaces over totally real fields are potentially modular
We show that abelian surfaces (and consequently curves of genus 2) over totally real fields
are potentially modular. As a consequence, we obtain the expected meromorphic …
are potentially modular. As a consequence, we obtain the expected meromorphic …
On the generic part of the cohomology of non-compact unitary Shimura varieties
A Caraiani, P Scholze - arXiv preprint arXiv:1909.01898, 2019 - arxiv.org
We prove that the generic part of the mod l cohomology of Shimura varieties associated to
quasi-split unitary groups of even dimension is concentrated above the middle degree …
quasi-split unitary groups of even dimension is concentrated above the middle degree …
The Ramanujan and Sato-Tate Conjectures for Bianchi modular forms
We prove the Ramanujan and Sato-Tate conjectures for Bianchi modular forms of weight at
least 2. More generally, we prove these conjectures for all regular algebraic cuspidal …
least 2. More generally, we prove these conjectures for all regular algebraic cuspidal …
Supersymmetric flux compactifications and Calabi-Yau modularity
Flux compactification of IIB string theory associates special points in Calabi-Yau moduli
space to choices of (pairs of) integral three-form fluxes. In this paper, we propose that …
space to choices of (pairs of) integral three-form fluxes. In this paper, we propose that …
Patching and the completed homology of locally symmetric spaces
Under an assumption on the existence of p-adic Galois representations, we carry out Taylor–
Wiles patching (in the derived category) for the completed homology of the locally symmetric …
Wiles patching (in the derived category) for the completed homology of the locally symmetric …
Machine-learning the Sato–Tate conjecture
We apply some of the latest techniques from machine-learning to the arithmetic of
hyperelliptic curves. More precisely we show that, with impressive accuracy and confidence …
hyperelliptic curves. More precisely we show that, with impressive accuracy and confidence …
Adjoint Selmer groups of automorphic Galois representations of unitary type.
J Newton, JA Thorne - Journal of the European Mathematical Society …, 2023 - ems.press
Let be the p-adic Galois representation attached to a cuspidal, regular algebraic
automorphic representation of GLn of unitary type. Under very mild hypotheses on, we prove …
automorphic representation of GLn of unitary type. Under very mild hypotheses on, we prove …
On the generic part of the cohomology of local and global Shimura varieties
T Koshikawa - arXiv preprint arXiv:2106.10602, 2021 - arxiv.org
Using the work of Fargues-Scholze, we prove a vanishing theorem for the generic
unramified part of the cohomology of local Shimura varieties of general linear groups. This …
unramified part of the cohomology of local Shimura varieties of general linear groups. This …
On the étale cohomology of Hilbert modular varieties with torsion coefficients
A Caraiani, M Tamiozzo - Compositio Mathematica, 2023 - cambridge.org
We study the étale cohomology of Hilbert modular varieties, building on the methods
introduced by Caraiani and Scholze for unitary Shimura varieties. We obtain the analogous …
introduced by Caraiani and Scholze for unitary Shimura varieties. We obtain the analogous …
Derived Hecke algebra and cohomology of arithmetic groups
A Venkatesh - Forum of Mathematics, Pi, 2019 - cambridge.org
DERIVED HECKE ALGEBRA AND COHOMOLOGY OF ARITHMETIC GROUPS Page 1 Forum
of Mathematics, Pi (2019), Vol. 7, e7, 119 pages doi:10.1017/fmp.2019.6 1 DERIVED HECKE …
of Mathematics, Pi (2019), Vol. 7, e7, 119 pages doi:10.1017/fmp.2019.6 1 DERIVED HECKE …