Chapter 29: Arithmetic geometry of toric varieties. Metrics, measures and heights 000S

Gil, José Ignacio Burgos; Philippon, Patrice; Sombra, Martín

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Statements and objects

Theorem 1.2 . [02IE]
Definition 2.1 . [02IH]
Example 2.2 . [02II]
Definition 2.3 . [02IJ]
Example 2.4 . [02IK]
Remark 2.5 . [02IL]
Definition 2.6 . [02IN]
Theorem 2.7 . [02IP]
Proof. [02IQ]
Example 2.8 . [02IR]
Remark 2.9 . [02IS]
Definition 2.10 . [02IU]
Definition 2.11 . [02IV]
Definition 2.16 . [02IW]
Definition 2.17 . [02IX]
Proposition 2.18 . [02IY]
Proof. [02IZ]
Proposition 2.19 . [02J0]
Proof. [02J1]
Proposition 2.21 . [02J2]
Proof. [02J3]
Proposition 2.23 . [02J4]
Proof. [02J5]
Example 2.24 . [02J6]
Example 2.25 . [02J7]
Definition 2.26 . [02J8]
Example 2.27 . [02J9]
Definition 2.28 . [02JA]
Remark 2.30 . [02JB]
Definition 2.31 . [02JD]
Example 2.32 . [02JE]
Proposition 2.33 . [02JF]
Proof. [02JG]
Definition 2.34 . [02JH]
Proposition 2.35 . [02JI]
Proof. [02JJ]
Proposition 2.36 . [02JK]
Proof. [02JL]
Proposition 2.37 . [02JM]
Proof. [02JN]
Definition 2.38 . [02JP]
Definition 2.39 . [02JQ]
Remark 2.41 . [02JR]
Remark 2.42 . [02JS]
Remark 2.44 . [02JT]
Remark 2.45 . [02JU]
Theorem 2.46 . [02JV]
Proof. [02JW]
Definition 2.47 . [02JY]
Definition 2.48 . [02JZ]
Example 2.49 . [02K0]
Example 2.50 . [02K1]
Definition 2.51 . [02K2]
Definition 2.52 . [02K3]
Definition 2.53 . [02K4]
Proposition 2.55 . [02K5]
Proof. [02K6]
Definition 2.56 . [02K7]
Theorem 2.57 . [02K8]
Proof. [02K9]
Definition 3.1 . [02KC]
Definition 3.2 . [02KD]
Definition 3.3 . [02KE]
Definition 3.6 . [02KF]
Definition 3.7 . [02KG]
Example 3.8 . [02KH]
Proposition 3.9 . [02KI]
Proof. [02KJ]
Definition 3.10 . [02KK]
Lemma 3.11 . [02KL]
Proof. [02KM]
Definition 3.12 . [02KN]
Definition 3.13 . [02KP]
Remark 3.14 . [02KQ]
Corollary 3.15 . [02KR]
Proof. [02KS]
Example 3.16 . [02KU]
Proposition 3.17 . [02KV]
Proof. [02KW]
Proposition 3.18 . [02KX]
Proof. [02KY]
Proposition 3.21 . [02KZ]
Proof. [02L0]
Definition 3.23 . [02L1]
Lemma 3.24 . [02L2]
Proof. [02L3]
Proposition 3.26 . [02L4]
Proof. [02L5]
Proposition 3.27 . [02L6]
Proof. [02L7]
Lemma 3.28 . [02L8]
Proof. [02L9]
Definition 3.31 . [02LA]
Definition 3.32 . [02LB]
Theorem 3.33 . [02LC]
Proof. [02LD]
Definition 3.34 . [02LE]
Example 3.36 . [02LF]
Example 3.37 . [02LG]
Proposition 3.38 . [02LI]
Proof. [02LJ]
Remark 3.39 . [02LK]
Proposition 3.40 . [02LL]
Proof. [02LM]
Lemma 3.41 . [02LN]
Proof. [02LP]
Definition 3.42 . [02LQ]
Proposition 3.43 . [02LR]
Proof. [02LS]
Proposition 3.45 . [02LT]
Proof. [02LU]
Proposition 3.46 . [02LV]
Proof. [02LW]
Definition 3.48 . [02LX]
Proposition 3.50 . [02LY]
Proof. [02LZ]
Definition 3.51 . [02M1]
Theorem 3.52 . [02M2]
Proof. [02M3]
Example 3.53 . [02M4]
Proposition 3.55 . [02M5]
Proof. [02M6]
Example 3.57 . [02M7]
Definition 3.58 . [02M9]
Lemma 3.59 . [02MA]
Proof. [02MB]
Definition 3.60 . [02MC]
Proposition 3.64 . [02MD]
Proof. [02ME]
Example 3.65 . [02MF]
Definition 3.66 . [02MG]
Definition 3.67 . [02MH]
Definition 3.68 . [02MI]
Proposition 3.69 . [02MJ]
Proof. [02MK]
Example 3.70 . [02ML]
Example 3.71 . [02MM]
Proposition 3.72 . [02MN]
Proof. [02MP]
Definition 3.73 . [02MQ]
Remark 3.74 . [02MR]
Proposition 3.75 . [02MS]
Proof. [02MT]
Example 3.76 . [02MU]
Proposition 3.77 . [02MV]
Proof. [02MW]
Proposition 3.78 . [02MX]
Proof. [02MY]
Lemma 3.79 . [02MZ]
Proof. [02N0]
Proposition 3.80 . [02N1]
Proof. [02N2]
Proposition 3.81 . [02N3]
Proof. [02N4]
Definition 3.82 . [02N6]
Proposition 3.83 . [02N7]
Proof. [02N8]
Corollary 3.84 . [02N9]
Proof. [02NA]
Definition 3.85 . [02NB]
Proposition 3.87 . [02NC]
Proof. [02ND]
Definition 3.88 . [02NE]
Proposition 3.89 . [02NF]
Proof. [02NG]
Definition 3.90 . [02NH]
Proposition 3.91 . [02NI]
Proof. [02NJ]
Definition 3.92 . [02NL]
Proposition 3.93 . [02NM]
Proof. [02NN]
Proposition 3.94 . [02NP]
Proof. [02NQ]
Proposition 3.95 . [02NR]
Proof. [02NS]
Example 3.96 . [02NT]
Theorem 3.97 . [02NU]
Proof. [02NV]
Definition 3.102 . [02NW]
Notation 3.103 . [02NX]
Corollary 3.104 . [02NY]
Proof. [02NZ]
Example 3.106 . [02P0]
Definition 3.107 . [02P1]
Proposition 3.108 . [02P2]
Proof. [02P3]
Definition 3.109 . [02P4]
Proposition 3.111 . [02P5]
Proof. [02P6]
Corollary 3.112 . [02P7]
Proof. [02P8]
Definition 3.113 . [02P9]
Definition 4.1 . [02PC]
Theorem 4.2 . [02PD]
Proof. [02PE]
Example 4.3 . [02PF]
Proposition 4.6 . [02PH]
Proof. [02PI]
Definition 4.7 . [02PJ]
Theorem 4.9 . [02PK]
Proof. [02PL]
Example 4.10 . [02PM]
Definition 4.12 . [02PN]
Example 4.13 . [02PP]
Definition 4.14 . [02PR]
Definition 4.15 . [02PS]
Theorem 4.18 . [02PT]
Proof. [02PU]
Definition 4.19 . [02PV]
Remark 4.20 . [02PW]
Remark 4.21 . [02PX]
Theorem 4.22 . [02PY]
Proof. [02PZ]
Notation 4.23 . [02Q0]
Definition 4.24 . [02Q1]
Example 4.26 . [02Q2]
Theorem 4.27 . [02Q3]
Proof. [02Q4]
Remark 4.28 . [02Q5]
Corollary 4.29 . [02Q6]
Proof. [02Q7]
Proposition 4.31 . [02Q8]
Proof. [02Q9]
Example 4.32 . [02QA]
Proposition 4.34 . [02QB]
Proposition 4.35 . [02QC]
Remark 4.36 . [02QD]
Proposition 4.37 . [02QF]
Proof. [02QG]
Remark 4.40 . [02QH]
Definition 4.41 . [02QI]
Theorem 4.42 . [02QJ]
Proof. [02QK]
Remark 4.43 . [02QL]
Example 4.44 . [02QM]
Proposition 4.45 . [02QN]
Proof. [02QP]
Proposition 4.46 . [02QQ]
Proof. [02QR]
Proposition 4.47 . [02QS]
Proof. [02QT]
Corollary 4.52 . [02QU]
Proof. [02QV]
Example 4.53 . [02QW]
Theorem 4.54 . [02QX]
Proof. [02QY]
Definition 4.55 . [02R0]
Definition 4.56 . [02R1]
Theorem 4.59 . [02R2]
Proof. [02R3]
Theorem 4.60 . [02R4]
Proof. [02R5]
Example 4.62 . [02R6]
Definition 4.63 . [02R7]
Proposition 4.64 . [02R8]
Proof. [02R9]
Proposition 4.65 . [02RA]
Proof. [02RB]
Remark 4.66 . [02RC]
Remark 4.67 . [02RD]
Definition 4.68 . [02RE]
Lemma 4.69 . [02RF]
Proof. [02RG]
Definition 4.70 . [02RH]
Definition 4.71 . [02RI]
Proposition 4.72 . [02RJ]
Proof. [02RK]
Definition 4.74 . [02RM]
Example 4.75 . [02RN]
Definition 4.76 . [02RP]
Definition 4.77 . [02RQ]
Proposition 4.78 . [02RR]
Proposition-Definition 4.79 . [02RS]
Proof. [02RT]
Theorem 4.80 . [02RU]
Proof. [02RV]
Theorem 4.81 . [02RW]
Proof. [02RX]
Remark 4.83 . [02RY]
Proposition 4.84 . [02RZ]
Proof. [02S0]
Example 4.86 . [02S1]
Proposition 4.89 . [02S2]
Proof. [02S3]
Proposition 4.91 . [02S4]
Proof. [02S5]
Example 4.92 . [02S6]
Proposition 4.94 . [02S7]
Theorem 4.95 . [02S9]
Proof. [02SA]
Definition 4.96 . [02SB]
Theorem 4.97 . [02SC]
Proof. [02SD]
Corollary 4.98 . [02SE]
Proof. [02SF]
Proposition 4.99 . [02SG]
Proof. [02SH]
Lemma 4.102 . [02SI]
Proof. [02SJ]
Proposition 4.103 . [02SK]
Proof. [02SL]
Proposition 4.105 . [02SM]
Proof. [02SN]
Remark 4.107 . [02SP]
Proposition 4.108 . [02SQ]
Proof. [02SR]
Example 4.109 . [02SS]
Lemma 5.1 . [02SV]
Proof. [02SW]
Proposition-Definition 5.2 . [02SX]
Proof. [02SY]
Remark 5.8 . [02SZ]
Proposition 5.9 . [02T0]
Proposition 5.10 . [02T1]
Proposition 5.11 . [02T3]
Proof. [02T4]
Definition 5.12 . [02T5]
Definition 5.14 . [02T6]
Proposition 5.16 . [02T7]
Proof. [02T8]
Corollary 5.17 . [02T9]
Proof. [02TA]
Example 5.18 . [02TB]
Proposition 5.19 . [02TC]
Proof. [02TD]
Proposition-Definition 5.20 . [02TE]
Proof. [02TF]
Proposition 5.21 . [02TG]
Proof. [02TH]
Proposition 5.22 . [02TI]
Proof. [02TJ]
Corollary 5.23 . [02TK]
Proof. [02TL]
Proposition 5.24 . [02TM]
Corollary 5.25 . [02TN]
Example 5.26 . [02TP]
Proposition 5.27 . [02TQ]
Proof. [02TR]
Corollary 5.28 . [02TS]
Proof. [02TT]
Proposition 5.29 . [02TV]
Proof. [02TW]
Definition 5.32 . [02TX]
Theorem 5.33 . [02TY]
Proof. [02TZ]
Proposition 5.38 . [02U0]
Proof. [02U1]
Lemma 5.39 . [02U3]
Proof. [02U4]
Corollary 5.40 . [02U5]
Proof. [02U6]
Proposition 5.41 . [02U7]
Proof. [02U8]
Example 5.42 . [02U9]
Corollary 5.43 . [02UA]
Proof. [02UB]
Example 5.44 . [02UC]
Question 5.45 . [02UD]
Remark 5.46 . [02UE]
Corollary 5.47 . [02UF]
Proof. [02UG]
Lemma 5.48 . [02UH]
Proof. [02UI]
Theorem 5.49 . [02UJ]
Proof. [02UK]
Proposition 5.51 . [02UL]
Proof. [02UM]
Proposition 5.52 . [02UN]
Proof. [02UP]
Proposition 5.53 . [02UQ]
Proof. [02UR]
Definition 5.54 . [02UT]
Proposition 5.55 . [02UU]
Proof. [02UV]
Lemma 5.56 . [02UW]
Proof. [02UX]
Lemma 5.57 . [02UY]
Proof. [02UZ]
Lemma 5.58 . [02V0]
Proof. [02V1]
Lemma 5.60 . [02V2]
Proof. [02V3]
Proposition 5.61 . [02V4]
Proof. [02V5]
Proposition 5.63 . [02V6]
Proof. [02V7]
Corollary 5.65 . [02V8]
Proof. [02V9]
Corollary 5.66 . [02VA]
Proof. [02VB]
Proposition 5.67 . [02VD]
Proof. [02VE]
Corollary 5.68 . [02VF]
Proof. [02VG]
Corollary 5.69 . [02VH]
Theorem 5.70 . [02VI]
Proof. [02VJ]
Theorem 5.73 . [02VL]
Proof. [02VM]
Remark 5.74 . [02VN]
Proposition 5.75 . [02VP]
Proof. [02VQ]
Proposition 5.80 . [02VR]
Proof. [02VS]
Theorem 5.81 . [02VT]
Proof. [02VU]
Corollary 5.83 . [02VV]
Definition 5.84 . [02VX]
Theorem 5.85 . [02VY]
Proof. [02VZ]
Corollary 5.86 . [02W0]
Proof. [02W1]
Definition 6.1 . [02W4]
Remark 6.3 . [02W5]
Proposition 6.4 . [02W6]
Proof. [02W7]
Theorem 6.6 . [02W8]
Definition 6.8 . [02W9]
Proof of Theorem 6.6 . [02WA]
Remark 6.16 . [02WB]
Corollary 6.17 . [02WC]
Proof. [02WD]
Corollary 6.21 . [02WE]
Proof. [02WF]
Remark 6.23 . [02WG]
Proposition 6.24 . [02WH]
Proof. [02WI]
Proposition 6.25 . [02WJ]
Proof. [02WK]
Proposition 6.27 . [02WL]
Proof. [02WM]
Corollary 6.30 . [02WN]
Example 6.31 . [02WP]
Definition 6.32 . [02WR]
Remark 6.33 . [02WS]
Remark 6.34 . [02WT]
Proposition 6.35 . [02WU]
Proof. [02WV]
Theorem 6.37 . [02WW]
Proof. [02WX]
Corollary 6.39 . [02WY]
Proof. [02WZ]
Remark 6.40 . [02X0]
Definition 7.1 . [02X3]
Proposition 7.3 . [02X4]
Proof. [02X5]
Corollary 7.7 . [02X6]
Proof. [02X7]
Proposition 7.8 . [02X8]
Proof. [02X9]
Example 7.10 . [02XA]
Corollary 7.14 . [02XB]
Proof. [02XC]
Proposition 7.15 . [02XD]
Proof. [02XE]
Lemma 7.18 . [02XF]
Proof. [02XG]
Corollary 7.19 . [02XH]
Proof. [02XI]
Lemma 7.21 . [02XK]
Proof. [02XL]
Definition 7.23 . [02XM]
Example 7.24 . [02XN]
Remark 7.26 . [02XP]
Proposition 7.27 . [02XQ]
Proof. [02XR]
Example 7.29 . [02XS]
Example 7.30 . [02XT]
Remark 7.33 . [02XU]
Proposition 7.34 . [02XV]
Proof. [02XW]
Example 7.35 . [02XX]
Remark 7.36 . [02XY]
Proposition 8.1 . [02Y1]
Proof. [02Y2]
Lemma 8.6 . [02Y3]
Proof. [02Y4]
Theorem 8.7 . [02Y5]
Remark 8.8 . [02Y6]
Proof. [02Y7]
Corollary 8.12 . [02Y8]
Proof. [02Y9]
Corollary 8.13 . [02YA]
Proof. [02YB]
Corollary 8.16 . [02YC]
Proof. [02YD]
Lemma 8.17 . [02YF]
Proof. [02YG]
Corollary 8.19 . [02YH]
Proposition 8.20 . [02YI]
Proof. [02YJ]
Lemma 8.22 . [02YK]
Proof. [02YL]
Proposition 8.26 . [02YM]
Proof. [02YN]
Remark 8.27 . [02YP]

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Chapter 29: Arithmetic geometry of toric varieties. Metrics, measures and heights 000S

Statements and objects

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