國立虎尾科技大學 |

Construction of Anticyclotomic Euler Systems Using Diagonal Cycles.

紀錄類型:	書目-語言資料,手稿 : Monograph/item
正題名/作者:	Construction of Anticyclotomic Euler Systems Using Diagonal Cycles./
作者:	Alonso Rodriguez, Raul.
面頁冊數:	1 online resource (185 pages)
附註:	Source: Dissertations Abstracts International, Volume: 84-12, Section: B.
Contained By:	Dissertations Abstracts International84-12B.
標題:	Applied mathematics. -
電子資源:	click for full text (PQDT)
ISBN:	9798379718206

Construction of Anticyclotomic Euler Systems Using Diagonal Cycles.
Alonso Rodriguez, Raul.

Construction of Anticyclotomic Euler Systems Using Diagonal Cycles. - 1 online resource (185 pages)

Source: Dissertations Abstracts International, Volume: 84-12, Section: B.

Thesis (Ph.D.)--Princeton University, 2023.

Includes bibliographical references

In this thesis, we construct a new anticyclotomic Euler system for the four-dimensional Galois representation attached to two modular forms and a Hecke character of an imaginary quadratic field. To state the results more precisely, let g and h be newforms of weights l ≥ m of the same parity and let ψ be a Hecke character of an imaginary quadratic field K of infinity-type (1 − k, 0) for some even integer k ≥ 2. Assume that the product of the characters of g, h and the CM-form attached to ψ is trivial. Let p be a prime which splits in K. We then study the p-adic GK-representation V := Vg ⊗ Vh(ψ−1 )(1 − c), where c = (k + l + m − 2)/2. Combining a geometric construction using modified diagonal cycles in the product of three modular curves with a result of Lei-Loeffler-Zerbes, we obtain cohomology classes over ring class field extensions of K, and we prove that they form a split anticyclotomic Euler system in the sense of Jetchev-Nekovar-Skinner.The bottom Λ-adic class of our Euler system is related to a one-variable specialization of the triple product p-adic L-function constructed by Darmon-Rotger via a reciprocity law proved by Bertolini-Seveso-Venerucci and Darmon-Rotger. This reciprocity law, together with the Euler-system machinery developed by Jetchev- Nekovar-Skinner, allows us to deduce, under some additional hypotheses, different cases of the Bloch-Kato conjecture for the representation V in analytic rank zero and one. As a different application, we also give two equivalent formulations of an Iwasawa-Greenberg Main Conjecture in this setting and prove one divisibility.When h = g∗, i.e., the modular form obtained by conjugating the Fourier coefficients of g, we obtain an Euler system for the three-dimensional GK-representation V' := ad0 (Vg)(ψ −1 )(1 − k/2) ⊂ V and use it to derive similar applications towards the Bloch-Kato conjecture in analytic rank zero and one and towards a divisibility of an Iwasawa-Greenberg Main Conjecture.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2024

Mode of access: World Wide Web

ISBN: 9798379718206Subjects--Topical Terms:

1069907
Applied mathematics.
Subjects--Index Terms:

Euler systemsIndex Terms--Genre/Form:

554714
Electronic books.

Construction of Anticyclotomic Euler Systems Using Diagonal Cycles.
LDR:03329ntm a22003857 4500 001 1142031
005 20240414211926.5
006 m o d
007 cr mn ---uuuuu
008 250605s2023 xx obm 000 0 eng d
020 $a 9798379718206
035 $a (MiAaPQ)AAI30490630
035 $a AAI30490630
040 $a MiAaPQ $b eng $c MiAaPQ $d NTU
100 1 $a Alonso Rodriguez, Raul. $3 1466178
245 1 0 $a Construction of Anticyclotomic Euler Systems Using Diagonal Cycles.
264 0 $c 2023
300 $a 1 online resource (185 pages)
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
500 $a Source: Dissertations Abstracts International, Volume: 84-12, Section: B.
500 $a Advisor: Skinner, Christopher.
502 $a Thesis (Ph.D.)--Princeton University, 2023.
504 $a Includes bibliographical references
520 $a In this thesis, we construct a new anticyclotomic Euler system for the four-dimensional Galois representation attached to two modular forms and a Hecke character of an imaginary quadratic field. To state the results more precisely, let g and h be newforms of weights l ≥ m of the same parity and let ψ be a Hecke character of an imaginary quadratic field K of infinity-type (1 − k, 0) for some even integer k ≥ 2. Assume that the product of the characters of g, h and the CM-form attached to ψ is trivial. Let p be a prime which splits in K. We then study the p-adic GK-representation V := Vg ⊗ Vh(ψ−1 )(1 − c), where c = (k + l + m − 2)/2. Combining a geometric construction using modified diagonal cycles in the product of three modular curves with a result of Lei-Loeffler-Zerbes, we obtain cohomology classes over ring class field extensions of K, and we prove that they form a split anticyclotomic Euler system in the sense of Jetchev-Nekovar-Skinner.The bottom Λ-adic class of our Euler system is related to a one-variable specialization of the triple product p-adic L-function constructed by Darmon-Rotger via a reciprocity law proved by Bertolini-Seveso-Venerucci and Darmon-Rotger. This reciprocity law, together with the Euler-system machinery developed by Jetchev- Nekovar-Skinner, allows us to deduce, under some additional hypotheses, different cases of the Bloch-Kato conjecture for the representation V in analytic rank zero and one. As a different application, we also give two equivalent formulations of an Iwasawa-Greenberg Main Conjecture in this setting and prove one divisibility.When h = g∗, i.e., the modular form obtained by conjugating the Fourier coefficients of g, we obtain an Euler system for the three-dimensional GK-representation V' := ad0 (Vg)(ψ −1 )(1 − k/2) ⊂ V and use it to derive similar applications towards the Bloch-Kato conjecture in analytic rank zero and one and towards a divisibility of an Iwasawa-Greenberg Main Conjecture.
533 $a Electronic reproduction. $b Ann Arbor, Mich. : $c ProQuest, $d 2024
538 $a Mode of access: World Wide Web
650 4 $a Applied mathematics. $3 1069907
650 4 $a Mathematics. $3 527692
653 $a Euler systems
653 $a Iwasawa theory
653 $a Euler system
653 $a Quadratic field
653 $a Cohomology
655 7 $a Electronic books. $2 local $3 554714
690 $a 0405
690 $a 0364
710 2 $a Princeton University. $b Mathematics. $3 1180706
710 2 $a ProQuest Information and Learning Co. $3 1178819
773 0 $t Dissertations Abstracts International $g 84-12B.
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=30490630 $z click for full text (PQDT)