?ュ??瀛﹁??锛?Hideto Asashiba

?ュ??????浣?锛?????澶у?/浜??藉ぇ瀛 楂?绛???绌堕??/span>

?ュ???堕?达?2024骞?1??8? 涓??? 14:30-16:30

?ュ???扮?癸?寤鸿?烘ゼ209

?ュ????瑕?锛?Let G be a finitely generated right A-module for a finite-dimensional algebra A over a fieled k, and I the additive closure of G. We will define an I-relative Koszul coresolution K^.(V ) of an indecomposable direct summand V of G, and show that for a finitely generated A-module M, the I-relative i-th Betti number for M at V is given as the k-dimension of the i-th homology of the I-relative Koszul complex K_V(M)_. := Hom_A(K^.(V), M) of M at V for all i ? 0. This is applied to investigate the minimal interval resolution/coresolution of a persistence module M, e.g., to check the interval decomposability of M, and to compute the interval approximation of M

?ュ??瀛﹁??绠?浠?锛?Hideto Asashiba???????ユ??????澶у??ｈ???浼?????锛?浜??藉ぇ瀛︽?板???绌朵腑蹇?涓?澶ч???绔?澶у?????绌跺????2024骞存?ユ???板?浼?浠ｆ?板?濂????峰??????ㄥ??虹?浠风???????规?????绌跺??寰?浜?涓?绯诲????褰卞??????缁??????朵腑?充?Grothendieck??????瀵煎?虹?浠风??缁?????琛ㄥ??/span>Adv. Math. 235(2013), 134-160???ㄥ??虹?浠枫??绋冲?绛?浠蜂?Gabriel 瑕?????璁虹?稿?虫?归?㈢????绌讹?澶?浜???娌垮?颁?????浠??充?寰?????娆¤???????寸??瀵煎?鸿???寸??绮?????Grothendieck????????浣?宸茬?瀹???锛?涓?涓?姝ワ???浠??涓?姝ョ??绌惰??归?㈢???稿?抽?????甯?????璇?ideto Asashiba????锛?甯???????ideto Asashiba?????ㄥ??虹?浠蜂?瑕?????璁虹????????缁?楠?锛??ㄥ??虹?浠蜂?瑕?????璁虹??绌剁兢璁恒??