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Autor: Michele Fornea, Xavier Guitart, Marc Masdeu

Publikováno v: Advances in Mathematics. 406:108484

For modular elliptic curves over number fields of narrow class number one, and with multiplicative reduction at a collection of p-adic primes, we define new p-adic invariants. Inspired by Nekovar and Scholl's plectic conjectures, we believe these inv

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::d65a8c8ed2c71ec6964e527427b9d171
https://doi.org/10.1016/j.aim.2022.108484

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A quaternionic construction of p-adic singular moduli

Autor: Xavier Guitart, Xavier Xarles, Marc Masdeu

Publikováno v: Research in the Mathematical Sciences. 8

Rigid meromorphic cocycles were introduced by Darmon and Vonk as a conjectural p-adic extension of the theory of singular moduli to real quadratic base fields. They are certain cohomology classes of $${{\,\mathrm{SL}\,}}_2(\mathbb {Z}[1/p])$$ which c

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::ffae7be5b34d53c28a96d7b730630182
https://doi.org/10.1007/s40687-021-00274-3

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Computing 𝑝-adic periods of abelian varieties from automorphic forms

Autor: Marc Masdeu, Xavier Guitart

Publikováno v: Automorphic Forms and Related Topics. :75-83

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::ef31e2cdcb07b82e980eb9dd051224f4
https://doi.org/10.1090/conm/732/14787

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Poincaré duality isomorphisms in tensor categories

Autor: Marc Masdeu, Marco Adamo Seveso

Publikováno v: Journal of Pure and Applied Algebra. 222:3075-3123

If for a vector space V of dimension g over a characteristic zero field we denote by ∧ i V ∧ i V its alternating powers, and by V ∨ V ∨ its linear dual, then there are natural Poincare isomorphisms: ∧ i V ∨ ≅∧ g−i V. ∧ i V ∨ ≅

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::d36189ac05a8041a82b6212a01ec262a
https://doi.org/10.1016/j.jpaa.2017.11.015

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Dirac operators in tensor categories and the motive of quaternionic modular forms

Autor: Marco Adamo Seveso, Marc Masdeu

Publikováno v: Advances in Mathematics. 313:628-688

We define a motive whose realizations afford modular forms (of arbitrary weight) on an indefinite division quaternion algebra. This generalizes work of Iovita--Spiess to odd weights in the spirit of Jordan--Livn\'e. It also generalizes a construction

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::1ba5e3d19475a202aa7377af6b5bd2c2
https://doi.org/10.1016/j.aim.2017.03.034

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An automorphic approach to Darmon points

Autor: Marc Masdeu, Xavier Guitart, Santiago Molina

Publikováno v: UPCommons. Portal del coneixement obert de la UPC
Universitat Politècnica de Catalunya (UPC)

We give archimedean and non-archimedean constructions of Darmon points on modular abelian varieties attached to automorphic forms over arbitrary number fields and possibly non-trivial central character. An effort is made to present a unifying point o

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::53edbaedb428af10c9401c0d43d91c8e
http://hdl.handle.net/2445/193425

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Uniformization of modular elliptic curves via p-adic periods

Autor: Mehmet Haluk Sengun, Xavier Guitart, Marc Masdeu

Publikováno v: Journal of Algebra

The Langlands Programme predicts that a weight 2 newform f over a number field K with integer Hecke eigenvalues generally should have an associated elliptic curve E_f over K. In our previous paper, we associated, building on works of Darmon and Green

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::300027c9d5fad160864877a538b970f5
https://doi.org/10.1016/j.jalgebra.2015.06.021

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Computing fundamental domains for the Bruhat–Tits tree for , -adic automorphic forms, and the canonical embedding of Shimura curves

Autor: Marc Masdeu, Cameron Franc

Publikováno v: LMS Journal of Computation and Mathematics. 17:1-23

We describe algorithms that allow the computation of fundamental domains in the Bruhat–Tits tree for the action of discrete groups arising from quaternion algebras. These algorithms are used to compute spaces of rigid modular forms of arbitrary eve

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::2ff37244420af14ecbb28f9329ccf415
https://doi.org/10.1112/s1461157013000235

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Periods of Modular GL2-type Abelian Varieties and p-adic Integration

Autor: Xavier Guitart, Marc Masdeu

Publikováno v: Dipòsit Digital de la UB
Universidad de Barcelona
Experimental Mathematics
Recercat. Dipósit de la Recerca de Catalunya
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Let F be a number field and N an integral ideal in its ring of integers. Let f be a modular newform over F of level Gamma0(N) with rational Fourier coefficients. Under certain additional conditions, Guitart-Masdeu-Sengun constructed a p-adic lattice

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::5177eac4a77e16b526cccaf2e623ff0f
http://hdl.handle.net/2445/142925

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